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Least common denominator:
x^4/4+x+2+x^4/4+x+2
(x*(x-1)^2)^(1/3)*((x-1)^2/3+x*(-2+2*x)/3)/(x*(x-1)^2)
(x/sqrt(x^2-8))-(7*x/(x^2-8+7*(sqrt(x^2-8))))
sqrt(a)/(4-a)/a^(1/4)/(2-a^(1/2))
Factor polynomial:
y^5-32
x1*x2+x1^2*x3^2+x2*x3
a^8+b^8
a^5+b^5
Factor squared:
-y^2-4*y-3
3*x^2+5*x-3
-y^2+4*y-3
y^4+y^2+5
How do you in partial fractions?:
((y-9)/(y-8))*((y^2-64)/(y^2-16*y+64))
(5*a^2+3*a-2)/(a^2-1)
(a^2-9)/(15+5*a)
((3*c+1)/(c-1)+c)/(c+1)
Identical expressions
x^ four / four +x+ two +x^ four / four +x+ two
x to the power of 4 divide by 4 plus x plus 2 plus x to the power of 4 divide by 4 plus x plus 2
x to the power of four divide by four plus x plus two plus x to the power of four divide by four plus x plus two
x4/4+x+2+x4/4+x+2
x⁴/4+x+2+x⁴/4+x+2
x^4 divide by 4+x+2+x^4 divide by 4+x+2
Similar expressions
x^4/4+x+2+x^4/4+x-2
x^4/4+x+2+x^4/4-x+2
x^4/4-x+2+x^4/4+x+2
x^4/4+x-2+x^4/4+x+2
x^4/4+x+2-x^4/4+x+2

Expression simplification/ Least common denominator/ x^4/4+x+2+x^4/4+x+2

Least common denominator x^4/4+x+2+x^4/4+x+2

The solution

You have entered [src]

 4            4        
x            x         
-- + x + 2 + -- + x + 2
4            4

$$\left(x + \left(\frac{x^{4}}{4} + \left(\left(\frac{x^{4}}{4} + x\right) + 2\right)\right)\right) + 2$$

x^4/4 + x + 2 + x^4/4 + x + 2

General simplification [src]

     4      
    x       
4 + -- + 2*x
    2

$$\frac{x^{4}}{2} + 2 x + 4$$

4 + x^4/2 + 2*x

Fraction decomposition [src]

4 + x^4/2 + 2*x

$$\frac{x^{4}}{2} + 2 x + 4$$

     4      
    x       
4 + -- + 2*x
    2

Factorization [src]

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|                                                                                /          /      I*\/ 1455                                   8                                            16           | |                                                                                  /                                   8                                      /      I*\/ 1455                16           | |                                                                                  /                                   8                                      /      I*\/ 1455                16           | |                  /          /      I*\/ 1455                                   8                                            16                                                                           |
|                                                                               /    - 2*3 /   1 + ----------  + ------------------------------------------------------------- - ----------------------- | |                                                                                 /    - ------------------------------------------------------------- - 2*3 /   1 + ----------  - ----------------------- | |                                                                                 /    - ------------------------------------------------------------- - 2*3 /   1 + ----------  - ----------------------- | |                 /    - 2*3 /   1 + ----------  + ------------------------------------------------------------- - -----------------------                                                                 |
|              ___________________________________________________             /         \/            9                   ___________________________________________________          ________________ | |                ___________________________________________________             /                 ___________________________________________________     \/            9                ________________ | |                ___________________________________________________             /                 ___________________________________________________     \/            9                ________________ | |                /         \/            9                   ___________________________________________________          ________________              ___________________________________________________|
|             /        ________________                                       /                                           /        ________________                                    /         ______  | |               /        ________________                                       /                 /        ________________                                                              /         ______  | |               /        ________________                                       /                 /        ________________                                                              /         ______  | |               /                                           /        ________________                                    /         ______              /        ________________                           |
|            /        /         ______                                       /                                           /        /         ______                                    /      I*\/ 1455   | |              /        /         ______                                       /                 /        /         ______                                                              /      I*\/ 1455   | |              /        /         ______                                       /                 /        /         ______                                                              /      I*\/ 1455   | |              /                                           /        /         ______                                    /      I*\/ 1455              /        /         ______                            |
|           /        /      I*\/ 1455                16                     /                                           /        /      I*\/ 1455                16              3*3 /   1 + ----------  | |             /        /      I*\/ 1455                16                     /                 /        /      I*\/ 1455                16                                        3*3 /   1 + ----------  | |             /        /      I*\/ 1455                16                     /                 /        /      I*\/ 1455                16                                        3*3 /   1 + ----------  | |             /                                           /        /      I*\/ 1455                16              3*3 /   1 + ----------            /        /      I*\/ 1455                16           |
|          /    2*3 /   1 + ----------  + -----------------------          /                                           /    2*3 /   1 + ----------  + -----------------------      \/            9       | |            /    2*3 /   1 + ----------  + -----------------------          /                 /    2*3 /   1 + ----------  + -----------------------                                \/            9       | |            /    2*3 /   1 + ----------  + -----------------------          /                 /    2*3 /   1 + ----------  + -----------------------                                \/            9       | |            /                                           /    2*3 /   1 + ----------  + -----------------------      \/            9                /    2*3 /   1 + ----------  + ----------------------- |
|         /       \/            9                ________________         /                                           /       \/            9                ________________                            | |           /       \/            9                ________________         /                 /       \/            9                ________________                                                      | |           /       \/            9                ________________         /                 /       \/            9                ________________                                                      | |           /                                           /       \/            9                ________________                                    /       \/            9                ________________ |
|        /                                      /         ______         /                                           /                                      /         ______                             | |          /                                      /         ______         /                 /                                      /         ______                                                       | |          /                                      /         ______         /                 /                                      /         ______                                                       | |          /                                           /                                      /         ______                                    /                                      /         ______  |
|       /                                      /      I*\/ 1455         /                                           /                                      /      I*\/ 1455                              | |         /                                      /      I*\/ 1455         /                 /                                      /      I*\/ 1455                                                        | |         /                                      /      I*\/ 1455         /                 /                                      /      I*\/ 1455                                                        | |         /                                           /                                      /      I*\/ 1455                                    /                                      /      I*\/ 1455   |
|      /                                  3*3 /   1 + ----------       /                                           /                                  3*3 /   1 + ----------                             | |        /                                  3*3 /   1 + ----------       /                 /                                  3*3 /   1 + ----------                                                       | |        /                                  3*3 /   1 + ----------       /                 /                                  3*3 /   1 + ----------                                                       | |        /                                           /                                  3*3 /   1 + ----------                                  /                                  3*3 /   1 + ----------  |
|    \/                                     \/            9          \/                                          \/                                     \/            9                                  | |      \/                                     \/            9          \/                \/                                     \/            9                                                            | |      \/                                     \/            9          \/                \/                                     \/            9                                                            | |      \/                                          \/                                     \/            9                                     \/                                     \/            9       |
|x + ------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------|*|x + - ------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------|*|x + - ------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------|*|x + - ------------------------------------------------------------------------------------------------------------------------------------ + -------------------------------------------------------------|
\                                  2                                                                                                  2                                                                  / \                                    2                                                                                                  2                                                                  / \                                    2                                                                                                  2                                                                  / \                                                                       2                                                                                                   2                              /

$$\left(x + \left(\frac{\sqrt{- 2 \sqrt[3]{1 + \frac{\sqrt{1455} i}{9}} - \frac{8}{\sqrt{\frac{16}{3 \sqrt[3]{1 + \frac{\sqrt{1455} i}{9}}} + 2 \sqrt[3]{1 + \frac{\sqrt{1455} i}{9}}}} - \frac{16}{3 \sqrt[3]{1 + \frac{\sqrt{1455} i}{9}}}}}{2} - \frac{\sqrt{\frac{16}{3 \sqrt[3]{1 + \frac{\sqrt{1455} i}{9}}} + 2 \sqrt[3]{1 + \frac{\sqrt{1455} i}{9}}}}{2}\right)\right) \left(x + \left(\frac{\sqrt{- 2 \sqrt[3]{1 + \frac{\sqrt{1455} i}{9}} + \frac{8}{\sqrt{\frac{16}{3 \sqrt[3]{1 + \frac{\sqrt{1455} i}{9}}} + 2 \sqrt[3]{1 + \frac{\sqrt{1455} i}{9}}}} - \frac{16}{3 \sqrt[3]{1 + \frac{\sqrt{1455} i}{9}}}}}{2} + \frac{\sqrt{\frac{16}{3 \sqrt[3]{1 + \frac{\sqrt{1455} i}{9}}} + 2 \sqrt[3]{1 + \frac{\sqrt{1455} i}{9}}}}{2}\right)\right) \left(x + \left(- \frac{\sqrt{\frac{16}{3 \sqrt[3]{1 + \frac{\sqrt{1455} i}{9}}} + 2 \sqrt[3]{1 + \frac{\sqrt{1455} i}{9}}}}{2} - \frac{\sqrt{- 2 \sqrt[3]{1 + \frac{\sqrt{1455} i}{9}} - \frac{8}{\sqrt{\frac{16}{3 \sqrt[3]{1 + \frac{\sqrt{1455} i}{9}}} + 2 \sqrt[3]{1 + \frac{\sqrt{1455} i}{9}}}} - \frac{16}{3 \sqrt[3]{1 + \frac{\sqrt{1455} i}{9}}}}}{2}\right)\right) \left(x + \left(\frac{\sqrt{\frac{16}{3 \sqrt[3]{1 + \frac{\sqrt{1455} i}{9}}} + 2 \sqrt[3]{1 + \frac{\sqrt{1455} i}{9}}}}{2} - \frac{\sqrt{- 2 \sqrt[3]{1 + \frac{\sqrt{1455} i}{9}} + \frac{8}{\sqrt{\frac{16}{3 \sqrt[3]{1 + \frac{\sqrt{1455} i}{9}}} + 2 \sqrt[3]{1 + \frac{\sqrt{1455} i}{9}}}} - \frac{16}{3 \sqrt[3]{1 + \frac{\sqrt{1455} i}{9}}}}}{2}\right)\right)$$

(((x + sqrt(2*(1 + i*sqrt(1455)/9)^(1/3) + 16/(3*(1 + i*sqrt(1455)/9)^(1/3)))/2 + sqrt(-2*(1 + i*sqrt(1455)/9)^(1/3) + 8/sqrt(2*(1 + i*sqrt(1455)/9)^(1/3) + 16/(3*(1 + i*sqrt(1455)/9)^(1/3))) - 16/(3*(1 + i*sqrt(1455)/9)^(1/3)))/2)*(x - sqrt(2*(1 + i*sqrt(1455)/9)^(1/3) + 16/(3*(1 + i*sqrt(1455)/9)^(1/3)))/2 + sqrt(-8/sqrt(2*(1 + i*sqrt(1455)/9)^(1/3) + 16/(3*(1 + i*sqrt(1455)/9)^(1/3))) - 2*(1 + i*sqrt(1455)/9)^(1/3) - 16/(3*(1 + i*sqrt(1455)/9)^(1/3)))/2))*(x - sqrt(2*(1 + i*sqrt(1455)/9)^(1/3) + 16/(3*(1 + i*sqrt(1455)/9)^(1/3)))/2 - sqrt(-8/sqrt(2*(1 + i*sqrt(1455)/9)^(1/3) + 16/(3*(1 + i*sqrt(1455)/9)^(1/3))) - 2*(1 + i*sqrt(1455)/9)^(1/3) - 16/(3*(1 + i*sqrt(1455)/9)^(1/3)))/2))*(x - sqrt(-2*(1 + i*sqrt(1455)/9)^(1/3) + 8/sqrt(2*(1 + i*sqrt(1455)/9)^(1/3) + 16/(3*(1 + i*sqrt(1455)/9)^(1/3))) - 16/(3*(1 + i*sqrt(1455)/9)^(1/3)))/2 + sqrt(2*(1 + i*sqrt(1455)/9)^(1/3) + 16/(3*(1 + i*sqrt(1455)/9)^(1/3)))/2)

Common denominator [src]

     4      
    x       
4 + -- + 2*x
    2

$$\frac{x^{4}}{2} + 2 x + 4$$

4 + x^4/2 + 2*x

Powers [src]

     4      
    x       
4 + -- + 2*x
    2

$$\frac{x^{4}}{2} + 2 x + 4$$

4 + x^4/2 + 2*x

Trigonometric part [src]

     4      
    x       
4 + -- + 2*x
    2

$$\frac{x^{4}}{2} + 2 x + 4$$

4 + x^4/2 + 2*x

Assemble expression [src]

     4      
    x       
4 + -- + 2*x
    2

$$\frac{x^{4}}{2} + 2 x + 4$$

4 + x^4/2 + 2*x

Numerical answer [src]

4.0 + 2*x + 0.5*x^4

4.0 + 2*x + 0.5*x^4

Combining rational expressions [src]

      4           /     3\
16 + x  + 4*x + x*\4 + x /
--------------------------
            4

$$\frac{x^{4} + x \left(x^{3} + 4\right) + 4 x + 16}{4}$$

(16 + x^4 + 4*x + x*(4 + x^3))/4

Combinatorics [src]

     4      
    x       
4 + -- + 2*x
    2

$$\frac{x^{4}}{2} + 2 x + 4$$

4 + x^4/2 + 2*x

Rational denominator [src]

        4      
16 + 2*x  + 8*x
---------------
       4

$$\frac{2 x^{4} + 8 x + 16}{4}$$

(16 + 2*x^4 + 8*x)/4

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Identical expressions

Similar expressions

Least common denominator x^4/4+x+2+x^4/4+x+2

The solution