Mister Exam

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

An expression to simplify:

### 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
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