Mister Exam

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Least common denominator:
a/(a+b)+a^2/(b^2-a^2)
(z+y*(x*z)/(z^2-x*y)+x*(z*y)/(z^2-x*y)-2*z*((x*z)/(z^2-x*y))*((z*y)/(z^2-x*y)))/(z^2-x*y)
z-2/4*z^2+16*z+16/(z/2*z-4-z^2+4/2*z^2-8-2/z^2+2*z)
sqrt(a)-(a-1/a^2)/(sqrt(a)-1/sqrt(a))+(1-1/a^2)/(sqrt(a)+1/(sqrt(a)))+2/a^(3/2)
Factor polynomial:
x^2+x-2
x^4+x^3
x^4+4
x^3+y^3
Factor squared:
y^4+9*y^2-5
-y^4-8*y^2-8
-y^2-2*y*b+b^2
x^2+x+6
How do you in partial fractions?:
150/(1+150*((15*150)/(151*(1/10p+1))+(15/(260*(5p^2+p)))))
(z/(z+6)*(z+6))-(z/(z-6)*(z+6))
(a^2-9)/(15+5*a)
b^9*b^7*b^2/(b^3*b^(1^9)*b^8)
Identical expressions
(z+y*(x*z)/(z^ two -x*y)+x*(z*y)/(z^ two -x*y)- two *z*((x*z)/(z^ two -x*y))*((z*y)/(z^ two -x*y)))/(z^ two -x*y)
(z plus y multiply by (x multiply by z) divide by (z squared minus x multiply by y) plus x multiply by (z multiply by y) divide by (z squared minus x multiply by y) minus 2 multiply by z multiply by ((x multiply by z) divide by (z squared minus x multiply by y)) multiply by ((z multiply by y) divide by (z squared minus x multiply by y))) divide by (z squared minus x multiply by y)
(z plus y multiply by (x multiply by z) divide by (z to the power of two minus x multiply by y) plus x multiply by (z multiply by y) divide by (z to the power of two minus x multiply by y) minus two multiply by z multiply by ((x multiply by z) divide by (z to the power of two minus x multiply by y)) multiply by ((z multiply by y) divide by (z to the power of two minus x multiply by y))) divide by (z to the power of two minus x multiply by y)
(z+y*(x*z)/(z2-x*y)+x*(z*y)/(z2-x*y)-2*z*((x*z)/(z2-x*y))*((z*y)/(z2-x*y)))/(z2-x*y)
z+y*x*z/z2-x*y+x*z*y/z2-x*y-2*z*x*z/z2-x*y*z*y/z2-x*y/z2-x*y
(z+y*(x*z)/(z²-x*y)+x*(z*y)/(z²-x*y)-2*z*((x*z)/(z²-x*y))*((z*y)/(z²-x*y)))/(z²-x*y)
(z+y*(x*z)/(z to the power of 2-x*y)+x*(z*y)/(z to the power of 2-x*y)-2*z*((x*z)/(z to the power of 2-x*y))*((z*y)/(z to the power of 2-x*y)))/(z to the power of 2-x*y)
(z+y(xz)/(z^2-xy)+x(zy)/(z^2-xy)-2z((xz)/(z^2-xy))((zy)/(z^2-xy)))/(z^2-xy)
(z+y(xz)/(z2-xy)+x(zy)/(z2-xy)-2z((xz)/(z2-xy))((zy)/(z2-xy)))/(z2-xy)
z+yxz/z2-xy+xzy/z2-xy-2zxz/z2-xyzy/z2-xy/z2-xy
z+yxz/z^2-xy+xzy/z^2-xy-2zxz/z^2-xyzy/z^2-xy/z^2-xy
(z+y*(x*z) divide by (z^2-x*y)+x*(z*y) divide by (z^2-x*y)-2*z*((x*z) divide by (z^2-x*y))*((z*y) divide by (z^2-x*y))) divide by (z^2-x*y)
Similar expressions
(z+y*(x*z)/(z^2-x*y)+x*(z*y)/(z^2-x*y)+2*z*((x*z)/(z^2-x*y))*((z*y)/(z^2-x*y)))/(z^2-x*y)
(z+y*(x*z)/(z^2-x*y)+x*(z*y)/(z^2-x*y)-2*z*((x*z)/(z^2+x*y))*((z*y)/(z^2-x*y)))/(z^2-x*y)
(z+y*(x*z)/(z^2-x*y)-x*(z*y)/(z^2-x*y)-2*z*((x*z)/(z^2-x*y))*((z*y)/(z^2-x*y)))/(z^2-x*y)
(z-y*(x*z)/(z^2-x*y)+x*(z*y)/(z^2-x*y)-2*z*((x*z)/(z^2-x*y))*((z*y)/(z^2-x*y)))/(z^2-x*y)
(z+y*(x*z)/(z^2-x*y)+x*(z*y)/(z^2-x*y)-2*z*((x*z)/(z^2-x*y))*((z*y)/(z^2+x*y)))/(z^2-x*y)
(z+y*(x*z)/(z^2-x*y)+x*(z*y)/(z^2-x*y)-2*z*((x*z)/(z^2-x*y))*((z*y)/(z^2-x*y)))/(z^2+x*y)
(z+y*(x*z)/(z^2+x*y)+x*(z*y)/(z^2-x*y)-2*z*((x*z)/(z^2-x*y))*((z*y)/(z^2-x*y)))/(z^2-x*y)
(z+y*(x*z)/(z^2-x*y)+x*(z*y)/(z^2+x*y)-2*z*((x*z)/(z^2-x*y))*((z*y)/(z^2-x*y)))/(z^2-x*y)

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

Least common denominator (z+y(xz)/(z^2-xy)+x(zy)/(z^2-xy)-2z((xz)/(z^2-xy))((zy)/(z^2-xy)))/(z^2-xy)

The solution

You have entered [src]

     y*x*z      x*z*y           x*z      z*y   
z + -------- + -------- - 2*z*--------*--------
     2          2              2        2      
    z  - x*y   z  - x*y       z  - x*y z  - x*y
-----------------------------------------------
                     2                         
                    z  - x*y

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

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

General simplification [src]

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

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

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

Numerical answer [src]

(z + 2*x*y*z/(z^2 - x*y) - 2.0*x*y*z^3/(z^2 - x*y)^2)/(z^2 - x*y)

(z + 2*x*y*z/(z^2 - x*y) - 2.0*x*y*z^3/(z^2 - x*y)^2)/(z^2 - x*y)

Assemble expression [src]

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

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

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

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

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

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

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

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

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

Combinatorics [src]

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

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

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

Combining rational expressions [src]

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

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

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

Powers [src]

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

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

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

Trigonometric part [src]

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

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

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

Common denominator [src]

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

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

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

Rational denominator [src]

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

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

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

Other calculators

How to use it?

Identical expressions

Similar expressions

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

The solution

Least common denominator (z+y(xz)/(z^2-xy)+x(zy)/(z^2-xy)-2z((xz)/(z^2-xy))((zy)/(z^2-xy)))/(z^2-xy)