Mister Exam

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

An expression to simplify:

### 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)
(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))