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Least common denominator:
((y^2-49)/(y^2-14*y+49))^4/((y+7)/(y-7))^4
x*((x-1)^2/x^2)*(2/x-2*(x-1)/x^2)/(x-1)
(x-sqrt(6)+8)/(4-sqrt(x))*(2+sqrt(x))*(4/(16+x^2)+x*(4+x)^2/(256-x^4))
(x-sin(2*x)/2)/2-2*cos(x)+x
Factor polynomial:
x-x^3+5*x^2/2
x-x^3/3+x^5/5+3*x^4/4
x-x^3/3+x^4/4
x-x^3+3*x^2
Factor squared:
-y^2+y-7
-y^2+y+9
-y^2-y-8
-y^2+y-5
How do you in partial fractions?:
(x^4-x^2)/(x-1)
x^2+1/(x^2)
(m-(14*m-49)/m)/(7/m-1)
e^x/(e^x+2)
Identical expressions
(x-sqrt(six)+ eight)/(four -sqrt(x))*(two +sqrt(x))*(four /(sixteen +x^ two)+x*(four +x)^ two /(two hundred and fifty-six -x^ four))
(x minus square root of (6) plus 8) divide by (4 minus square root of (x)) multiply by (2 plus square root of (x)) multiply by (4 divide by (16 plus x squared ) plus x multiply by (4 plus x) squared divide by (256 minus x to the power of 4))
(x minus square root of (six) plus eight) divide by (four minus square root of (x)) multiply by (two plus square root of (x)) multiply by (four divide by (sixteen plus x to the power of two) plus x multiply by (four plus x) to the power of two divide by (two hundred and fifty minus six minus x to the power of four))
(x-√(6)+8)/(4-√(x))*(2+√(x))*(4/(16+x^2)+x*(4+x)^2/(256-x^4))
(x-sqrt(6)+8)/(4-sqrt(x))*(2+sqrt(x))*(4/(16+x2)+x*(4+x)2/(256-x4))
x-sqrt6+8/4-sqrtx*2+sqrtx*4/16+x2+x*4+x2/256-x4
(x-sqrt(6)+8)/(4-sqrt(x))*(2+sqrt(x))*(4/(16+x²)+x*(4+x)²/(256-x⁴))
(x-sqrt(6)+8)/(4-sqrt(x))*(2+sqrt(x))*(4/(16+x to the power of 2)+x*(4+x) to the power of 2/(256-x to the power of 4))
(x-sqrt(6)+8)/(4-sqrt(x))(2+sqrt(x))(4/(16+x^2)+x(4+x)^2/(256-x^4))
(x-sqrt(6)+8)/(4-sqrt(x))(2+sqrt(x))(4/(16+x2)+x(4+x)2/(256-x4))
x-sqrt6+8/4-sqrtx2+sqrtx4/16+x2+x4+x2/256-x4
x-sqrt6+8/4-sqrtx2+sqrtx4/16+x^2+x4+x^2/256-x^4
(x-sqrt(6)+8) divide by (4-sqrt(x))*(2+sqrt(x))*(4 divide by (16+x^2)+x*(4+x)^2 divide by (256-x^4))
Similar expressions
(x-sqrt(6)+8)/(4-sqrt(x))*(2+sqrt(x))*(4/(16+x^2)+x*(4-x)^2/(256-x^4))
(x-sqrt(6)+8)/(4-sqrt(x))*(2+sqrt(x))*(4/(16-x^2)+x*(4+x)^2/(256-x^4))
(x-sqrt(6)+8)/(4+sqrt(x))*(2+sqrt(x))*(4/(16+x^2)+x*(4+x)^2/(256-x^4))
(x-sqrt(6)+8)/(4-sqrt(x))*(2+sqrt(x))*(4/(16+x^2)+x*(4+x)^2/(256+x^4))
(x-sqrt(6)-8)/(4-sqrt(x))*(2+sqrt(x))*(4/(16+x^2)+x*(4+x)^2/(256-x^4))
(x-sqrt(6)+8)/(4-sqrt(x))*(2+sqrt(x))*(4/(16+x^2)-x*(4+x)^2/(256-x^4))
(x+sqrt(6)+8)/(4-sqrt(x))*(2+sqrt(x))*(4/(16+x^2)+x*(4+x)^2/(256-x^4))
(x-sqrt(6)+8)/(4-sqrt(x))*(2-sqrt(x))*(4/(16+x^2)+x*(4+x)^2/(256-x^4))

Expression simplification/ Least common denominator/ (x-sqrt(6)+8)/(4-sqrt(x))*(2+sqrt(x))*(4/(16+x^2)+x*(4+x)^2/(256-x^4))

Least common denominator (x-sqrt(6)+8)/(4-sqrt(x))(2+sqrt(x))(4/(16+x^2)+x*(4+x)^2/(256-x^4))

The solution

You have entered [src]

      ___                 /                   2\
x - \/ 6  + 8 /      ___\ |   4      x*(4 + x) |
-------------*\2 + \/ x /*|------- + ----------|
        ___               |      2           4 |
  4 - \/ x                \16 + x     256 - x  /

$$\frac{\left(x - \sqrt{6}\right) + 8}{4 - \sqrt{x}} \left(\sqrt{x} + 2\right) \left(\frac{x \left(x + 4\right)^{2}}{256 - x^{4}} + \frac{4}{x^{2} + 16}\right)$$

(((x - sqrt(6) + 8)/(4 - sqrt(x)))*(2 + sqrt(x)))*(4/(16 + x^2) + (x*(4 + x)^2)/(256 - x^4))

General simplification [src]

/      ___\ /          ___\ /          4            2 /      2\\
\2 + \/ x /*\8 + x - \/ 6 /*\1024 - 4*x  + x*(4 + x) *\16 + x //
----------------------------------------------------------------
               /        4\ /       ___\ /      2\               
               \-256 + x /*\-4 + \/ x /*\16 + x /

$$\frac{\left(\sqrt{x} + 2\right) \left(x - \sqrt{6} + 8\right) \left(- 4 x^{4} + x \left(x + 4\right)^{2} \left(x^{2} + 16\right) + 1024\right)}{\left(\sqrt{x} - 4\right) \left(x^{2} + 16\right) \left(x^{4} - 256\right)}$$

(2 + sqrt(x))*(8 + x - sqrt(6))*(1024 - 4*x^4 + x*(4 + x)^2*(16 + x^2))/((-256 + x^4)*(-4 + sqrt(x))*(16 + x^2))

Assemble expression [src]

            /                   2\                
/      ___\ |   4      x*(4 + x) | /          ___\
\2 + \/ x /*|------- + ----------|*\8 + x - \/ 6 /
            |      2           4 |                
            \16 + x     256 - x  /                
--------------------------------------------------
                          ___                     
                    4 - \/ x

$$\frac{\left(\sqrt{x} + 2\right) \left(\frac{x \left(x + 4\right)^{2}}{256 - x^{4}} + \frac{4}{x^{2} + 16}\right) \left(x - \sqrt{6} + 8\right)}{4 - \sqrt{x}}$$

(2 + sqrt(x))*(4/(16 + x^2) + x*(4 + x)^2/(256 - x^4))*(8 + x - sqrt(6))/(4 - sqrt(x))

Combinatorics [src]

/      ___\ /          ___\
\2 + \/ x /*\8 + x - \/ 6 /
---------------------------
            /       ___\   
   (-4 + x)*\-4 + \/ x /

$$\frac{\left(\sqrt{x} + 2\right) \left(x - \sqrt{6} + 8\right)}{\left(\sqrt{x} - 4\right) \left(x - 4\right)}$$

(2 + sqrt(x))*(8 + x - sqrt(6))/((-4 + x)*(-4 + sqrt(x)))

Combining rational expressions [src]

/      ___\ /          ___\ /          4            2 /      2\\
\2 + \/ x /*\8 + x - \/ 6 /*\1024 - 4*x  + x*(4 + x) *\16 + x //
----------------------------------------------------------------
                /      ___\ /      2\ /       4\                
                \4 - \/ x /*\16 + x /*\256 - x /

$$\frac{\left(\sqrt{x} + 2\right) \left(x - \sqrt{6} + 8\right) \left(- 4 x^{4} + x \left(x + 4\right)^{2} \left(x^{2} + 16\right) + 1024\right)}{\left(4 - \sqrt{x}\right) \left(256 - x^{4}\right) \left(x^{2} + 16\right)}$$

(2 + sqrt(x))*(8 + x - sqrt(6))*(1024 - 4*x^4 + x*(4 + x)^2*(16 + x^2))/((4 - sqrt(x))*(16 + x^2)*(256 - x^4))

Numerical answer [src]

(2.0 + x^0.5)*(5.55051025721682 + x)*(4.0/(16.0 + x^2) + 16.0*x*(1 + 0.25*x)^2/(256.0 - x^4))/(4.0 - x^0.5)

(2.0 + x^0.5)*(5.55051025721682 + x)*(4.0/(16.0 + x^2) + 16.0*x*(1 + 0.25*x)^2/(256.0 - x^4))/(4.0 - x^0.5)

Rational denominator [src]

               ___        4        9/2       5       11/2      6         2         3/2                     ___    5        2          ___   ___            ___       ___  5      9/2        2       4        2        ___  9/2        ___  4       7/2        2       3        2       5/2        2        2        2        3/2        2                 2     ___  4        2           ___        2        ___  3/2        2        ___  2        2       ___  3        2       ___  7/2        2
65536 - 8192*\/ 6  - 256*x  - 192*x    - 64*x  - 24*x     - 4*x  + 1024*x  + 6144*x    + 16384*x + 49152*\/ x  + x *(4 + x)  - 6144*\/ 6 *\/ x  - 1024*x*\/ 6  + 4*\/ 6 *x  + 6*x   *(4 + x)  + 16*x *(4 + x)  + 24*\/ 6 *x    + 32*\/ 6 *x  + 48*x   *(4 + x)  + 80*x *(4 + x)  + 96*x   *(4 + x)  + 256*x *(4 + x)  + 768*x   *(4 + x)  + 1024*x*(4 + x)  - \/ 6 *x *(4 + x)  - 128*x*\/ 6 *(4 + x)  - 96*\/ 6 *x   *(4 + x)  - 16*\/ 6 *x *(4 + x)  - 8*\/ 6 *x *(4 + x)  - 6*\/ 6 *x   *(4 + x) 
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                                                  /        4\           /      2\                                                                                                                                                                                                                                   
                                                                                                                                                                                                                                  \-256 + x /*(-16 + x)*\16 + x /

$$\frac{- 24 x^{\frac{11}{2}} + 6 x^{\frac{9}{2}} \left(x + 4\right)^{2} - 192 x^{\frac{9}{2}} + 24 \sqrt{6} x^{\frac{9}{2}} - 6 \sqrt{6} x^{\frac{7}{2}} \left(x + 4\right)^{2} + 48 x^{\frac{7}{2}} \left(x + 4\right)^{2} + 96 x^{\frac{5}{2}} \left(x + 4\right)^{2} - 96 \sqrt{6} x^{\frac{3}{2}} \left(x + 4\right)^{2} + 768 x^{\frac{3}{2}} \left(x + 4\right)^{2} + 6144 x^{\frac{3}{2}} - 6144 \sqrt{6} \sqrt{x} + 49152 \sqrt{x} - 4 x^{6} + x^{5} \left(x + 4\right)^{2} - 64 x^{5} + 4 \sqrt{6} x^{5} - \sqrt{6} x^{4} \left(x + 4\right)^{2} + 16 x^{4} \left(x + 4\right)^{2} - 256 x^{4} + 32 \sqrt{6} x^{4} - 8 \sqrt{6} x^{3} \left(x + 4\right)^{2} + 80 x^{3} \left(x + 4\right)^{2} - 16 \sqrt{6} x^{2} \left(x + 4\right)^{2} + 256 x^{2} \left(x + 4\right)^{2} + 1024 x^{2} - 128 \sqrt{6} x \left(x + 4\right)^{2} + 1024 x \left(x + 4\right)^{2} - 1024 \sqrt{6} x + 16384 x - 8192 \sqrt{6} + 65536}{\left(x - 16\right) \left(x^{2} + 16\right) \left(x^{4} - 256\right)}$$

(65536 - 8192*sqrt(6) - 256*x^4 - 192*x^(9/2) - 64*x^5 - 24*x^(11/2) - 4*x^6 + 1024*x^2 + 6144*x^(3/2) + 16384*x + 49152*sqrt(x) + x^5*(4 + x)^2 - 6144*sqrt(6)*sqrt(x) - 1024*x*sqrt(6) + 4*sqrt(6)*x^5 + 6*x^(9/2)*(4 + x)^2 + 16*x^4*(4 + x)^2 + 24*sqrt(6)*x^(9/2) + 32*sqrt(6)*x^4 + 48*x^(7/2)*(4 + x)^2 + 80*x^3*(4 + x)^2 + 96*x^(5/2)*(4 + x)^2 + 256*x^2*(4 + x)^2 + 768*x^(3/2)*(4 + x)^2 + 1024*x*(4 + x)^2 - sqrt(6)*x^4*(4 + x)^2 - 128*x*sqrt(6)*(4 + x)^2 - 96*sqrt(6)*x^(3/2)*(4 + x)^2 - 16*sqrt(6)*x^2*(4 + x)^2 - 8*sqrt(6)*x^3*(4 + x)^2 - 6*sqrt(6)*x^(7/2)*(4 + x)^2)/((-256 + x^4)*(-16 + x)*(16 + x^2))

Powers [src]

            /                   2\                
/      ___\ |   4      x*(4 + x) | /          ___\
\2 + \/ x /*|------- + ----------|*\8 + x - \/ 6 /
            |      2           4 |                
            \16 + x     256 - x  /                
--------------------------------------------------
                          ___                     
                    4 - \/ x

$$\frac{\left(\sqrt{x} + 2\right) \left(\frac{x \left(x + 4\right)^{2}}{256 - x^{4}} + \frac{4}{x^{2} + 16}\right) \left(x - \sqrt{6} + 8\right)}{4 - \sqrt{x}}$$

(2 + sqrt(x))*(4/(16 + x^2) + x*(4 + x)^2/(256 - x^4))*(8 + x - sqrt(6))/(4 - sqrt(x))

Common denominator [src]

                                 ___         2         3/2         5/2         3        7/2        4        9/2       5       11/2      13/2          ___       ___  11/2       ___  5       ___  9/2        ___  4        ___  7/2         ___  3         ___  5/2         ___  2         ___  3/2            ___          ___   ___
  1   -49152 - 12288*x - 12288*\/ x  - 6144*x  - 6144*x    - 2304*x    - 1536*x  - 768*x    - 192*x  - 144*x    - 48*x  - 24*x     - 3*x     + 4096*\/ 6  + 2*\/ 6 *x     + 4*\/ 6 *x  + 8*\/ 6 *x    + 16*\/ 6 *x  + 64*\/ 6 *x    + 128*\/ 6 *x  + 256*\/ 6 *x    + 512*\/ 6 *x  + 512*\/ 6 *x    + 1024*x*\/ 6  + 2048*\/ 6 *\/ x 
- - + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
  2                                                                                                                                            2       9/2      13/2      6        4        5/2          ___                                                                                                                         
                                                                                                                                -32768 - 2048*x  - 32*x    - 2*x     + 8*x  + 128*x  + 512*x    + 8192*\/ x

$$- \frac{1}{2} + \frac{- 3 x^{\frac{13}{2}} - 24 x^{\frac{11}{2}} + 2 \sqrt{6} x^{\frac{11}{2}} - 144 x^{\frac{9}{2}} + 8 \sqrt{6} x^{\frac{9}{2}} - 768 x^{\frac{7}{2}} + 64 \sqrt{6} x^{\frac{7}{2}} - 2304 x^{\frac{5}{2}} + 256 \sqrt{6} x^{\frac{5}{2}} - 6144 x^{\frac{3}{2}} + 512 \sqrt{6} x^{\frac{3}{2}} - 12288 \sqrt{x} + 2048 \sqrt{6} \sqrt{x} - 48 x^{5} + 4 \sqrt{6} x^{5} - 192 x^{4} + 16 \sqrt{6} x^{4} - 1536 x^{3} + 128 \sqrt{6} x^{3} - 6144 x^{2} + 512 \sqrt{6} x^{2} - 12288 x + 1024 \sqrt{6} x - 49152 + 4096 \sqrt{6}}{- 2 x^{\frac{13}{2}} - 32 x^{\frac{9}{2}} + 512 x^{\frac{5}{2}} + 8192 \sqrt{x} + 8 x^{6} + 128 x^{4} - 2048 x^{2} - 32768}$$

-1/2 + (-49152 - 12288*x - 12288*sqrt(x) - 6144*x^2 - 6144*x^(3/2) - 2304*x^(5/2) - 1536*x^3 - 768*x^(7/2) - 192*x^4 - 144*x^(9/2) - 48*x^5 - 24*x^(11/2) - 3*x^(13/2) + 4096*sqrt(6) + 2*sqrt(6)*x^(11/2) + 4*sqrt(6)*x^5 + 8*sqrt(6)*x^(9/2) + 16*sqrt(6)*x^4 + 64*sqrt(6)*x^(7/2) + 128*sqrt(6)*x^3 + 256*sqrt(6)*x^(5/2) + 512*sqrt(6)*x^2 + 512*sqrt(6)*x^(3/2) + 1024*x*sqrt(6) + 2048*sqrt(6)*sqrt(x))/(-32768 - 2048*x^2 - 32*x^(9/2) - 2*x^(13/2) + 8*x^6 + 128*x^4 + 512*x^(5/2) + 8192*sqrt(x))

Trigonometric part [src]

            /                   2\                
/      ___\ |   4      x*(4 + x) | /          ___\
\2 + \/ x /*|------- + ----------|*\8 + x - \/ 6 /
            |      2           4 |                
            \16 + x     256 - x  /                
--------------------------------------------------
                          ___                     
                    4 - \/ x

$$\frac{\left(\sqrt{x} + 2\right) \left(\frac{x \left(x + 4\right)^{2}}{256 - x^{4}} + \frac{4}{x^{2} + 16}\right) \left(x - \sqrt{6} + 8\right)}{4 - \sqrt{x}}$$

(2 + sqrt(x))*(4/(16 + x^2) + x*(4 + x)^2/(256 - x^4))*(8 + x - sqrt(6))/(4 - sqrt(x))

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How to use it?

Identical expressions

Similar expressions

Least common denominator (x-sqrt(6)+8)/(4-sqrt(x))*(2+sqrt(x))*(4/(16+x^2)+x*(4+x)^2/(256-x^4))

The solution

Least common denominator (x-sqrt(6)+8)/(4-sqrt(x))(2+sqrt(x))(4/(16+x^2)+x*(4+x)^2/(256-x^4))