Mister Exam

Lang:

How to use it?
Least common denominator:
-2*sqrt(3)/(3*sqrt(1-(2*x-1)^2/3))
2/(a+2)+(a-2)/(a^2+4*a+4)/(a/(2*a-4)+(a^2+4)/(8-2*a)-2/(2*a+a^2))
(z+z/q)*(z-z/q)
z/(z+9)^2-z/(z^2-81)
Factor polynomial:
x^3-8
x^2+x-6
x^2+4
x^3+1
Factor squared:
y^4+y^2+3
-y^4+y^2+14
y^4-y^2+15
y^4-y^2+3
How do you in partial fractions?:
(z/c+c/z)/((z^2+c^2)/(5*z^9*c))
(x^2-9)/(x+3)
(x+5)/(x^2+22*x+85)
(x^2-x-12)/(x+3)
How do you in partial fractions?:
z/(z+9)^2-z/(z^2-81)
Identical expressions
z/(z+ nine)^ two -z/(z^ two - eighty-one)
z divide by (z plus 9) squared minus z divide by (z squared minus 81)
z divide by (z plus nine) to the power of two minus z divide by (z to the power of two minus eighty minus one)
z/(z+9)2-z/(z2-81)
z/z+92-z/z2-81
z/(z+9)²-z/(z²-81)
z/(z+9) to the power of 2-z/(z to the power of 2-81)
z/z+9^2-z/z^2-81
z divide by (z+9)^2-z divide by (z^2-81)
Similar expressions
z/(z+9)^2+z/(z^2-81)
z/(z-9)^2-z/(z^2-81)
z/(z+9)^2-z/(z^2+81)

Least common denominator z/(z+9)^2-z/(z^2-81)

You have entered [src]

   z          z   
-------- - -------
       2    2     
(z + 9)    z  - 81

$$- \frac{z}{z^{2} - 81} + \frac{z}{\left(z + 9\right)^{2}}$$

z/(z + 9)^2 - z/(z^2 - 81)

General simplification [src]

         -18*z         
-----------------------
        3             2
-729 + z  - 81*z + 9*z

$$- \frac{18 z}{z^{3} + 9 z^{2} - 81 z - 729}$$

-18*z/(-729 + z^3 - 81*z + 9*z^2)

Fraction decomposition [src]

1/(2*(9 + z)) - 9/(9 + z)^2 - 1/(2*(-9 + z))

$$\frac{1}{2 \left(z + 9\right)} - \frac{9}{\left(z + 9\right)^{2}} - \frac{1}{2 \left(z - 9\right)}$$

    1          9           1     
--------- - -------- - ----------
2*(9 + z)          2   2*(-9 + z)
            (9 + z)

Common denominator [src]

         -18*z         
-----------------------
        3             2
-729 + z  - 81*z + 9*z

$$- \frac{18 z}{z^{3} + 9 z^{2} - 81 z - 729}$$

-18*z/(-729 + z^3 - 81*z + 9*z^2)

Combinatorics [src]

      -18*z      
-----------------
                2
(-9 + z)*(9 + z)

$$- \frac{18 z}{\left(z - 9\right) \left(z + 9\right)^{2}}$$

-18*z/((-9 + z)*(9 + z)^2)

Numerical answer [src]

-z/(-81.0 + z^2) + 0.0123456790123457*z/(1 + 0.111111111111111*z)^2

-z/(-81.0 + z^2) + 0.0123456790123457*z/(1 + 0.111111111111111*z)^2

Combining rational expressions [src]

  /       2          2\
z*\-81 + z  - (9 + z) /
-----------------------
  /       2\        2  
  \-81 + z /*(9 + z)

$$\frac{z \left(z^{2} - \left(z + 9\right)^{2} - 81\right)}{\left(z + 9\right)^{2} \left(z^{2} - 81\right)}$$

z*(-81 + z^2 - (9 + z)^2)/((-81 + z^2)*(9 + z)^2)

Rational denominator [src]

  /       2\            2
z*\-81 + z / - z*(9 + z) 
-------------------------
   /       2\        2   
   \-81 + z /*(9 + z)

$$\frac{- z \left(z + 9\right)^{2} + z \left(z^{2} - 81\right)}{\left(z + 9\right)^{2} \left(z^{2} - 81\right)}$$

(z*(-81 + z^2) - z*(9 + z)^2)/((-81 + z^2)*(9 + z)^2)