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Least common denominator:
(z^5-5*z^3+10*z-1/10*z+1/5*z^3-1/z^5)*(z^3-3*z+1/3*z-1/z^3)
((x*x^(1/2)-x)^3)/((((x^(3/4)-1)/(x^(1/4)-1)-x^(1/2))*(1-x))^3)
factorial(x)*factorial(x)/factorial(x-2)/factorial(x-1)
x^4/4+x+2+x^4/4+x+2
Factor polynomial:
x^4-1
x^2-2
x^6*y^9-64*x^3
x^8-y^8
Factor squared:
-y^4-y^2+8
y^4+y^2+9
3*x^2+5*x-3
-y^2+4*y-3
How do you in partial fractions?:
y/(b*y-2*b^2)-2/(y^2+y-2*b*y-2*b)*(1+(3*y+y^2)/(3+y))
((p+3)/(p^2-2p))*((4p-8)/(p+3))
(((2s-2+2*s^2)/(-s*(2+s^2+2*s)))+((-2s^2+2s-6))/((s*(s^2+2*s+2))))*1/s-2/s
(a^2-9)/(15+5*a)
Identical expressions
((x*x^(one / two)-x)^ three)/((((x^(three / four)- one)/(x^(one / four)- one)-x^(one / two))*(one -x))^ three)
((x multiply by x to the power of (1 divide by 2) minus x) cubed ) divide by ((((x to the power of (3 divide by 4) minus 1) divide by (x to the power of (1 divide by 4) minus 1) minus x to the power of (1 divide by 2)) multiply by (1 minus x)) cubed )
((x multiply by x to the power of (one divide by two) minus x) to the power of three) divide by ((((x to the power of (three divide by four) minus one) divide by (x to the power of (one divide by four) minus one) minus x to the power of (one divide by two)) multiply by (one minus x)) to the power of three)
((x*x(1/2)-x)3)/((((x(3/4)-1)/(x(1/4)-1)-x(1/2))*(1-x))3)
x*x1/2-x3/x3/4-1/x1/4-1-x1/2*1-x3
((x*x^(1/2)-x)³)/((((x^(3/4)-1)/(x^(1/4)-1)-x^(1/2))*(1-x))³)
((x*x to the power of (1/2)-x) to the power of 3)/((((x to the power of (3/4)-1)/(x to the power of (1/4)-1)-x to the power of (1/2))*(1-x)) to the power of 3)
((xx^(1/2)-x)^3)/((((x^(3/4)-1)/(x^(1/4)-1)-x^(1/2))(1-x))^3)
((xx(1/2)-x)3)/((((x(3/4)-1)/(x(1/4)-1)-x(1/2))(1-x))3)
xx1/2-x3/x3/4-1/x1/4-1-x1/21-x3
xx^1/2-x^3/x^3/4-1/x^1/4-1-x^1/21-x^3
((x*x^(1 divide by 2)-x)^3) divide by ((((x^(3 divide by 4)-1) divide by (x^(1 divide by 4)-1)-x^(1 divide by 2))*(1-x))^3)
Similar expressions
((x*x^(1/2)-x)^3)/((((x^(3/4)+1)/(x^(1/4)-1)-x^(1/2))*(1-x))^3)
((x*x^(1/2)-x)^3)/((((x^(3/4)-1)/(x^(1/4)+1)-x^(1/2))*(1-x))^3)
((x*x^(1/2)-x)^3)/((((x^(3/4)-1)/(x^(1/4)-1)+x^(1/2))*(1-x))^3)
((x*x^(1/2)-x)^3)/((((x^(3/4)-1)/(x^(1/4)-1)-x^(1/2))*(1+x))^3)
((x*x^(1/2)+x)^3)/((((x^(3/4)-1)/(x^(1/4)-1)-x^(1/2))*(1-x))^3)

Expression simplification/ Least common denominator/ ((x*x^(1/2)-x)^3)/((((x^(3/4)-1)/(x^(1/4)-1)-x^(1/2))*(1-x))^3)

Least common denominator ((xx^(1/2)-x)^3)/((((x^(3/4)-1)/(x^(1/4)-1)-x^(1/2))(1-x))^3)

The solution

You have entered [src]

                     3        
        /    ___    \         
        \x*\/ x  - x/         
------------------------------
                             3
//  3/4            \        \ 
|| x    - 1     ___|        | 
||--------- - \/ x |*(1 - x)| 
||4 ___            |        | 
\\\/ x  - 1        /        /

$$\frac{\left(\sqrt{x} x - x\right)^{3}}{\left(\left(1 - x\right) \left(- \sqrt{x} + \frac{x^{\frac{3}{4}} - 1}{\sqrt[4]{x} - 1}\right)\right)^{3}}$$

(x*sqrt(x) - x)^3/(((x^(3/4) - 1)/(x^(1/4) - 1) - sqrt(x))*(1 - x))^3

General simplification [src]

            3           3
/     4 ___\  / 3/2    \ 
\-1 + \/ x / *\x    - x/ 
-------------------------
             3           
  /      ___\          3 
  \1 - \/ x / *(-1 + x)

$$\frac{\left(\sqrt[4]{x} - 1\right)^{3} \left(x^{\frac{3}{2}} - x\right)^{3}}{\left(1 - \sqrt{x}\right)^{3} \left(x - 1\right)^{3}}$$

(-1 + x^(1/4))^3*(x^(3/2) - x)^3/((1 - sqrt(x))^3*(-1 + x)^3)

Combining rational expressions [src]

                    3           3         
        /     4 ___\  / 3/2    \          
        \-1 + \/ x / *\x    - x/          
------------------------------------------
                                         3
       3 /      3/4     ___ /     4 ___\\ 
(1 - x) *\-1 + x    - \/ x *\-1 + \/ x //

$$\frac{\left(\sqrt[4]{x} - 1\right)^{3} \left(x^{\frac{3}{2}} - x\right)^{3}}{\left(1 - x\right)^{3} \left(x^{\frac{3}{4}} - \sqrt{x} \left(\sqrt[4]{x} - 1\right) - 1\right)^{3}}$$

(-1 + x^(1/4))^3*(x^(3/2) - x)^3/((1 - x)^3*(-1 + x^(3/4) - sqrt(x)*(-1 + x^(1/4)))^3)

Trigonometric part [src]

                    3           
          / 3/2    \            
          \x    - x/            
--------------------------------
                               3
         /                3/4 \ 
       3 |    ___   -1 + x    | 
(1 - x) *|- \/ x  + ----------| 
         |               4 ___| 
         \          -1 + \/ x /

$$\frac{\left(x^{\frac{3}{2}} - x\right)^{3}}{\left(1 - x\right)^{3} \left(- \sqrt{x} + \frac{x^{\frac{3}{4}} - 1}{\sqrt[4]{x} - 1}\right)^{3}}$$

(x^(3/2) - x)^3/((1 - x)^3*(-sqrt(x) + (-1 + x^(3/4))/(-1 + x^(1/4)))^3)

Expand expression [src]

                     3       
        /    ___    \        
        \x*\/ x  - x/        
-----------------------------
                            3
         /  3/4            \ 
       3 | x    - 1     ___| 
(1 - x) *|--------- - \/ x | 
         |4 ___            | 
         \\/ x  - 1        /

$$\frac{\left(\sqrt{x} x - x\right)^{3}}{\left(1 - x\right)^{3} \left(- \sqrt{x} + \frac{x^{\frac{3}{4}} - 1}{\sqrt[4]{x} - 1}\right)^{3}}$$

(x*sqrt(x) - x)^3/((1 - x)^3*((x^(3/4) - 1)/(x^(1/4) - 1) - sqrt(x))^3)

Rational denominator [src]

            3             3           3 
 /      ___\  /     4 ___\  / 3/2    \  
-\1 + \/ x / *\-1 + \/ x / *\x    - x/  
----------------------------------------
                       6                
               (-1 + x)

$$- \frac{\left(\sqrt[4]{x} - 1\right)^{3} \left(\sqrt{x} + 1\right)^{3} \left(x^{\frac{3}{2}} - x\right)^{3}}{\left(x - 1\right)^{6}}$$

-(1 + sqrt(x))^3*(-1 + x^(1/4))^3*(x^(3/2) - x)^3/(-1 + x)^6

Powers [src]

                    3           
          / 3/2    \            
          \x    - x/            
--------------------------------
                               3
         /                3/4 \ 
       3 |    ___   -1 + x    | 
(1 - x) *|- \/ x  + ----------| 
         |               4 ___| 
         \          -1 + \/ x /

$$\frac{\left(x^{\frac{3}{2}} - x\right)^{3}}{\left(1 - x\right)^{3} \left(- \sqrt{x} + \frac{x^{\frac{3}{4}} - 1}{\sqrt[4]{x} - 1}\right)^{3}}$$

(x^(3/2) - x)^3/((1 - x)^3*(-sqrt(x) + (-1 + x^(3/4))/(-1 + x^(1/4)))^3)

Assemble expression [src]

                    3           
          / 3/2    \            
          \x    - x/            
--------------------------------
                               3
         /                3/4 \ 
       3 |    ___   -1 + x    | 
(1 - x) *|- \/ x  + ----------| 
         |               4 ___| 
         \          -1 + \/ x /

$$\frac{\left(x^{\frac{3}{2}} - x\right)^{3}}{\left(1 - x\right)^{3} \left(- \sqrt{x} + \frac{x^{\frac{3}{4}} - 1}{\sqrt[4]{x} - 1}\right)^{3}}$$

(x^(3/2) - x)^3/((1 - x)^3*(-sqrt(x) + (-1 + x^(3/4))/(-1 + x^(1/4)))^3)

Numerical answer [src]

(x^1.5 - x)^3/((1.0 - x)^3*(-x^0.5 + (-1.0 + x^0.75)/(-1.0 + x^0.25))^3)

(x^1.5 - x)^3/((1.0 - x)^3*(-x^0.5 + (-1.0 + x^0.75)/(-1.0 + x^0.25))^3)

Combinatorics [src]

            3           3
/     4 ___\  /     3/2\ 
\-1 + \/ x / *\x - x   / 
-------------------------
                       3 
         3 /       ___\  
 (-1 + x) *\-1 + \/ x /

$$\frac{\left(\sqrt[4]{x} - 1\right)^{3} \left(- x^{\frac{3}{2}} + x\right)^{3}}{\left(\sqrt{x} - 1\right)^{3} \left(x - 1\right)^{3}}$$

(-1 + x^(1/4))^3*(x - x^(3/2))^3/((-1 + x)^3*(-1 + sqrt(x))^3)

Common denominator [src]

                    2       5/2        ___       15/4       7/2       9/2      21/4            11/2      13/4       17/4       3        3/2
  14       14 - 84*x  - 60*x    - 42*\/ x  - 24*x     - 18*x    - 10*x    - 3*x     + 3*x + 3*x     + 9*x     + 18*x     + 91*x  + 103*x   
- -- - x - --------------------------------------------------------------------------------------------------------------------------------
  3                                                 3       3/2      9/2       ___      4       2       5/2                                
                                           -3 - 24*x  - 24*x    - 3*x    + 9*\/ x  + 9*x  + 18*x  + 18*x

$$- x - \frac{14}{3} - \frac{- 3 x^{\frac{21}{4}} + 18 x^{\frac{17}{4}} - 24 x^{\frac{15}{4}} + 9 x^{\frac{13}{4}} + 3 x^{\frac{11}{2}} - 10 x^{\frac{9}{2}} - 18 x^{\frac{7}{2}} - 60 x^{\frac{5}{2}} + 103 x^{\frac{3}{2}} - 42 \sqrt{x} + 91 x^{3} - 84 x^{2} + 3 x + 14}{- 3 x^{\frac{9}{2}} + 18 x^{\frac{5}{2}} - 24 x^{\frac{3}{2}} + 9 \sqrt{x} + 9 x^{4} - 24 x^{3} + 18 x^{2} - 3}$$

-14/3 - x - (14 - 84*x^2 - 60*x^(5/2) - 42*sqrt(x) - 24*x^(15/4) - 18*x^(7/2) - 10*x^(9/2) - 3*x^(21/4) + 3*x + 3*x^(11/2) + 9*x^(13/4) + 18*x^(17/4) + 91*x^3 + 103*x^(3/2))/(-3 - 24*x^3 - 24*x^(3/2) - 3*x^(9/2) + 9*sqrt(x) + 9*x^4 + 18*x^2 + 18*x^(5/2))

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How to use it?

Identical expressions

Similar expressions

Least common denominator ((x*x^(1/2)-x)^3)/((((x^(3/4)-1)/(x^(1/4)-1)-x^(1/2))*(1-x))^3)

The solution

Least common denominator ((xx^(1/2)-x)^3)/((((x^(3/4)-1)/(x^(1/4)-1)-x^(1/2))(1-x))^3)