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Expression simplification/ Least common denominator/ (x*(x-6)^2)^(1/3)*((x-6)^2/3+x*(-12+2*x)/3)/(x*(x-6)^2)

Least common denominator (x*(x-6)^2)^(1/3)*((x-6)^2/3+x*(-12+2*x)/3)/(x*(x-6)^2)

An expression to simplify:

The solution

You have entered [src] 
   ____________ /       2                \
3 /          2  |(x - 6)    x*(-12 + 2*x)|
\/  x*(x - 6)  *|-------- + -------------|
                \   3             3      /
------------------------------------------
                         2                
                x*(x - 6)
$$\frac{\sqrt[3]{x \left(x - 6\right)^{2}} \left(\frac{x \left(2 x - 12\right)}{3} + \frac{\left(x - 6\right)^{2}}{3}\right)}{x \left(x - 6\right)^{2}}$$ 
((x*(x - 6)^2)^(1/3)*((x - 6)^2/3 + (x*(-12 + 2*x))/3))/((x*(x - 6)^2))
General simplification [src] 
   ____________________         
3 /   /      2       \          
\/  x*\36 + x  - 12*x/ *(-2 + x)
--------------------------------
           x*(-6 + x)
$$\frac{\sqrt[3]{x \left(x^{2} - 12 x + 36\right)} \left(x - 2\right)}{x \left(x - 6\right)}$$ 
(x*(36 + x^2 - 12*x))^(1/3)*(-2 + x)/(x*(-6 + x))
Common denominator [src] 
       ___________________        ___________________
    3 /  3       2             3 /  3       2        
- 2*\/  x  - 12*x  + 36*x  + x*\/  x  - 12*x  + 36*x 
-----------------------------------------------------
                        2                            
                       x  - 6*x
$$\frac{x \sqrt[3]{x^{3} - 12 x^{2} + 36 x} - 2 \sqrt[3]{x^{3} - 12 x^{2} + 36 x}}{x^{2} - 6 x}$$ 
(-2*(x^3 - 12*x^2 + 36*x)^(1/3) + x*(x^3 - 12*x^2 + 36*x)^(1/3))/(x^2 - 6*x)
Expand expression [src] 
   __________ /       2                \
3 /        2  |(x - 6)    x*(-12 + 2*x)|
\/  (x - 6)  *|-------- + -------------|
              \   3             3      /
----------------------------------------
              2/3        2              
             x   *(x - 6)
$$\frac{\left(\frac{x \left(2 x - 12\right)}{3} + \frac{\left(x - 6\right)^{2}}{3}\right) \sqrt[3]{\left(x - 6\right)^{2}}}{x^{\frac{2}{3}} \left(x - 6\right)^{2}}$$ 
((x - 6)^2)^(1/3)*((x - 6)^2/3 + (x*(-12 + 2*x))/3)/(x^(2/3)*(x - 6)^2)
Rational denominator [src] 
   _____________                            
3 /           2  /        2                \
\/  x*(-6 + x)  *\(-6 + x)  + x*(-12 + 2*x)/
--------------------------------------------
                           2                
               3*x*(-6 + x)
$$\frac{\sqrt[3]{x \left(x - 6\right)^{2}} \left(x \left(2 x - 12\right) + \left(x - 6\right)^{2}\right)}{3 x \left(x - 6\right)^{2}}$$ 
(x*(-6 + x)^2)^(1/3)*((-6 + x)^2 + x*(-12 + 2*x))/(3*x*(-6 + x)^2)
Combining rational expressions [src] 
   _____________         
3 /           2          
\/  x*(-6 + x)  *(-2 + x)
-------------------------
        x*(-6 + x)
$$\frac{\sqrt[3]{x \left(x - 6\right)^{2}} \left(x - 2\right)}{x \left(x - 6\right)}$$ 
(x*(-6 + x)^2)^(1/3)*(-2 + x)/(x*(-6 + x))
Combinatorics [src] 
   _____________         
3 /           2          
\/  x*(-6 + x)  *(-2 + x)
-------------------------
        x*(-6 + x)
$$\frac{\sqrt[3]{x \left(x - 6\right)^{2}} \left(x - 2\right)}{x \left(x - 6\right)}$$ 
(x*(-6 + x)^2)^(1/3)*(-2 + x)/(x*(-6 + x))
Numerical answer [src] 
0.0917202013581841*(x*(-1 + 0.166666666666667*x)^2)^0.333333333333333*(12.0*(-1 + 0.166666666666667*x)^2 + 0.333333333333333*x*(-12.0 + 2.0*x))/(x*(-1 + 0.166666666666667*x)^2)
0.0917202013581841*(x*(-1 + 0.166666666666667*x)^2)^0.333333333333333*(12.0*(-1 + 0.166666666666667*x)^2 + 0.333333333333333*x*(-12.0 + 2.0*x))/(x*(-1 + 0.166666666666667*x)^2)
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