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Least common denominator:
(z/b+b/z)/z^2+b^(2/7)*z^(16*b)
(z^5-5*z^3+10*z-10/z+5/z^3-1/z^5)*(z^3-3*z+3/z-1/z^3)
z/4*(x-y)-2*z/x-y
-z^3-(-1)*z^2*y*(-x)*z/(z^2+x*y)-y^2*x*(-x)*z/((z^2+x*y)*((z^2+x*y)^2))
Factor polynomial:
x^2+x^2
m^2-n^2
x^2-16
m^2+m-2
Factor squared:
-y^4+9*y^2-3
-y^4-9*y^2+15
y^4-8*y^2-9
-y^4-8*y^2+7
How do you in partial fractions?:
y/(y+3)+y/3+2/y
1/(x^4-1)
(10*x^3-15*a*x^2)/(21*a*x^3-14*x^4)
(x^2-6*x+8)/(x-4)
Identical expressions
-z^ three -(- one)*z^ two *y*(-x)*z/(z^ two +x*y)-y^ two *x*(-x)*z/((z^ two +x*y)*((z^ two +x*y)^ two))
minus z cubed minus ( minus 1) multiply by z squared multiply by y multiply by ( minus x) multiply by z divide by (z squared plus x multiply by y) minus y squared multiply by x multiply by ( minus x) multiply by z divide by ((z squared plus x multiply by y) multiply by ((z squared plus x multiply by y) squared ))
minus z to the power of three minus ( minus one) multiply by z to the power of two multiply by y multiply by ( minus x) multiply by z divide by (z to the power of two plus x multiply by y) minus y to the power of two multiply by x multiply by ( minus x) multiply by z divide by ((z to the power of two plus x multiply by y) multiply by ((z to the power of two plus x multiply by y) to the power of two))
-z3-(-1)*z2*y*(-x)*z/(z2+x*y)-y2*x*(-x)*z/((z2+x*y)*((z2+x*y)2))
-z3--1*z2*y*-x*z/z2+x*y-y2*x*-x*z/z2+x*y*z2+x*y2
-z³-(-1)*z²*y*(-x)*z/(z²+x*y)-y²*x*(-x)*z/((z²+x*y)*((z²+x*y)²))
-z to the power of 3-(-1)*z to the power of 2*y*(-x)*z/(z to the power of 2+x*y)-y to the power of 2*x*(-x)*z/((z to the power of 2+x*y)*((z to the power of 2+x*y) to the power of 2))
-z^3-(-1)z^2y(-x)z/(z^2+xy)-y^2x(-x)z/((z^2+xy)((z^2+xy)^2))
-z3-(-1)z2y(-x)z/(z2+xy)-y2x(-x)z/((z2+xy)((z2+xy)2))
-z3--1z2y-xz/z2+xy-y2x-xz/z2+xyz2+xy2
-z^3--1z^2y-xz/z^2+xy-y^2x-xz/z^2+xyz^2+xy^2
-z^3-(-1)*z^2*y*(-x)*z divide by (z^2+x*y)-y^2*x*(-x)*z divide by ((z^2+x*y)*((z^2+x*y)^2))
Similar expressions
-z^3-(-1)*z^2*y*(-x)*z/(z^2+x*y)+y^2*x*(-x)*z/((z^2+x*y)*((z^2+x*y)^2))
-z^3-(-1)*z^2*y*(-x)*z/(z^2-x*y)-y^2*x*(-x)*z/((z^2+x*y)*((z^2+x*y)^2))
-z^3+(-1)*z^2*y*(-x)*z/(z^2+x*y)-y^2*x*(-x)*z/((z^2+x*y)*((z^2+x*y)^2))
-z^3-(1)*z^2*y*(-x)*z/(z^2+x*y)-y^2*x*(-x)*z/((z^2+x*y)*((z^2+x*y)^2))
-z^3-(-1)*z^2*y*(-x)*z/(z^2+x*y)-y^2*x*(x)*z/((z^2+x*y)*((z^2+x*y)^2))
-z^3-(-1)*z^2*y*(-x)*z/(z^2+x*y)-y^2*x*(-x)*z/((z^2-x*y)*((z^2+x*y)^2))
z^3-(-1)*z^2*y*(-x)*z/(z^2+x*y)-y^2*x*(-x)*z/((z^2+x*y)*((z^2+x*y)^2))
-z^3-(-1)*z^2*y*(x)*z/(z^2+x*y)-y^2*x*(-x)*z/((z^2+x*y)*((z^2+x*y)^2))
-z^3-(-1)*z^2*y*(-x)*z/(z^2+x*y)-y^2*x*(-x)*z/((z^2+x*y)*((z^2-x*y)^2))

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

Least common denominator -z^3-(-1)z^2y*(-x)z/(z^2+xy)-y^2x(-x)z/((z^2+xy)((z^2+xy)^2))

The solution

You have entered [src]

         2                  2               
   3   -z *y*(-x)*z        y *x*(-x)*z      
- z  - ------------ - ----------------------
          2                                2
         z  + x*y     / 2      \ / 2      \ 
                      \z  + x*y/*\z  + x*y/

$$\left(- z^{3} - \frac{z - x y \left(- z^{2}\right)}{x y + z^{2}}\right) - \frac{z - x x y^{2}}{\left(x y + z^{2}\right) \left(x y + z^{2}\right)^{2}}$$

-z^3 - (((-z^2)*y)*(-x))*z/(z^2 + x*y) - ((y^2*x)*(-x))*z/((z^2 + x*y)*(z^2 + x*y)^2)

General simplification [src]

            2  2           3 
   3     z*x *y       x*y*z  
- z  + ----------- - --------
                 3    2      
       / 2      \    z  + x*y
       \z  + x*y/

$$\frac{x^{2} y^{2} z}{\left(x y + z^{2}\right)^{3}} - \frac{x y z^{3}}{x y + z^{2}} - z^{3}$$

-z^3 + z*x^2*y^2/(z^2 + x*y)^3 - x*y*z^3/(z^2 + x*y)

Expand expression [src]

         2                 2  2  
   3   -z *y*(-x)*z     z*x *y   
- z  - ------------ + -----------
          2                     3
         z  + x*y     / 2      \ 
                      \z  + x*y/

$$\frac{x^{2} y^{2} z}{\left(x y + z^{2}\right)^{3}} - z^{3} - \frac{z - x y \left(- z^{2}\right)}{x y + z^{2}}$$

-z^3 - (((-z^2)*y)*(-x))*z/(z^2 + x*y) + z*x^2*y^2/(z^2 + x*y)^3

Common denominator [src]

          9      2  2    2  2  5          7
     3   z  + z*x *y  + x *y *z  + 2*x*y*z 
- 2*z  + ----------------------------------
          6    3  3          4      2  2  2
         z  + x *y  + 3*x*y*z  + 3*x *y *z

$$- 2 z^{3} + \frac{x^{2} y^{2} z^{5} + x^{2} y^{2} z + 2 x y z^{7} + z^{9}}{x^{3} y^{3} + 3 x^{2} y^{2} z^{2} + 3 x y z^{4} + z^{6}}$$

-2*z^3 + (z^9 + z*x^2*y^2 + x^2*y^2*z^5 + 2*x*y*z^7)/(z^6 + x^3*y^3 + 3*x*y*z^4 + 3*x^2*y^2*z^2)

Trigonometric part [src]

            2  2           3 
   3     z*x *y       x*y*z  
- z  + ----------- - --------
                 3    2      
       / 2      \    z  + x*y
       \z  + x*y/

$$\frac{x^{2} y^{2} z}{\left(x y + z^{2}\right)^{3}} - \frac{x y z^{3}}{x y + z^{2}} - z^{3}$$

-z^3 + z*x^2*y^2/(z^2 + x*y)^3 - x*y*z^3/(z^2 + x*y)

Numerical answer [src]

-z^3 + z*x^2*y^2/(z^2 + x*y)^3 - x*y*z^3/(z^2 + x*y)

-z^3 + z*x^2*y^2/(z^2 + x*y)^3 - x*y*z^3/(z^2 + x*y)

Rational denominator [src]

          3                                                
/ 2      \  /   3 / 2      \        3\      2  2 / 2      \
\z  + x*y/ *\- z *\z  + x*y/ - x*y*z / + z*x *y *\z  + x*y/
-----------------------------------------------------------
                                  4                        
                        / 2      \                         
                        \z  + x*y/

$$\frac{x^{2} y^{2} z \left(x y + z^{2}\right) + \left(x y + z^{2}\right)^{3} \left(- x y z^{3} - z^{3} \left(x y + z^{2}\right)\right)}{\left(x y + z^{2}\right)^{4}}$$

((z^2 + x*y)^3*(-z^3*(z^2 + x*y) - x*y*z^3) + z*x^2*y^2*(z^2 + x*y))/(z^2 + x*y)^4

Combining rational expressions [src]

  /                     2               \
  | 2  2    2 / 2      \  /   2        \|
z*\x *y  + z *\z  + x*y/ *\- z  - 2*x*y//
-----------------------------------------
                         3               
               / 2      \                
               \z  + x*y/

$$\frac{z \left(x^{2} y^{2} + z^{2} \left(- 2 x y - z^{2}\right) \left(x y + z^{2}\right)^{2}\right)}{\left(x y + z^{2}\right)^{3}}$$

z*(x^2*y^2 + z^2*(z^2 + x*y)^2*(-z^2 - 2*x*y))/(z^2 + x*y)^3

Assemble expression [src]

                          2  2  
 3 /       x*y   \     z*x *y   
z *|-1 - --------| + -----------
   |      2      |             3
   \     z  + x*y/   / 2      \ 
                     \z  + x*y/

$$\frac{x^{2} y^{2} z}{\left(x y + z^{2}\right)^{3}} + z^{3} \left(- \frac{x y}{x y + z^{2}} - 1\right)$$

            2  2           3 
   3     z*x *y       x*y*z  
- z  + ----------- - --------
                 3    2      
       / 2      \    z  + x*y
       \z  + x*y/

$$\frac{x^{2} y^{2} z}{\left(x y + z^{2}\right)^{3}} - \frac{x y z^{3}}{x y + z^{2}} - z^{3}$$

-z^3 + z*x^2*y^2/(z^2 + x*y)^3 - x*y*z^3/(z^2 + x*y)

Combinatorics [src]

   / 8    2  2      3  3  2          6      2  2  4\ 
-z*\z  - x *y  + 2*x *y *z  + 4*x*y*z  + 5*x *y *z / 
-----------------------------------------------------
                               3                     
                     / 2      \                      
                     \z  + x*y/

$$- \frac{z \left(2 x^{3} y^{3} z^{2} + 5 x^{2} y^{2} z^{4} - x^{2} y^{2} + 4 x y z^{6} + z^{8}\right)}{\left(x y + z^{2}\right)^{3}}$$

-z*(z^8 - x^2*y^2 + 2*x^3*y^3*z^2 + 4*x*y*z^6 + 5*x^2*y^2*z^4)/(z^2 + x*y)^3

Powers [src]

            2  2           3 
   3     z*x *y       x*y*z  
- z  + ----------- - --------
                 3    2      
       / 2      \    z  + x*y
       \z  + x*y/

$$\frac{x^{2} y^{2} z}{\left(x y + z^{2}\right)^{3}} - \frac{x y z^{3}}{x y + z^{2}} - z^{3}$$

-z^3 + z*x^2*y^2/(z^2 + x*y)^3 - x*y*z^3/(z^2 + x*y)

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How to use it?

Identical expressions

Similar expressions

Least common denominator -z^3-(-1)*z^2*y*(-x)*z/(z^2+x*y)-y^2*x*(-x)*z/((z^2+x*y)*((z^2+x*y)^2))

The solution

Least common denominator -z^3-(-1)z^2y*(-x)z/(z^2+xy)-y^2x(-x)z/((z^2+xy)((z^2+xy)^2))