Mister Exam

Lang:

How to use it?
How do you in partial fractions?:
x/(x+1)^3
(x-6)/(x^2+36)
((x+5)/(x^2-81)+(x+7)/(x^2-18*x+81))/((x+3)^2)/((x+9)^2)+(7+x)/(9+x)
(x+5)/(x-5)+(x-5)/(x+5)
Factor polynomial:
y^2-1
x*y+y^2*x/15+3*x/x+y
x+y-x^2-y^2
x+y+x^2+y^2
Least common denominator:
x^2+12/x^2-4-x+2/x-2
(w^2/(5*a+w))-(25*a^2/(5*a+w))
t/(t+3)^3-3/(t+3)^3
t/(t+3)^3+3/(t+3)^3
Factor squared:
-y^4+3*y^2+6
-y^4+2*y^2+8
y^4-2*y^2+2
-y^4+2*y^2-12
Identical expressions
(x^ three - twenty-seven)/(x^ three - three *x+ nine)
(x cubed minus 27) divide by (x cubed minus 3 multiply by x plus 9)
(x to the power of three minus twenty minus seven) divide by (x to the power of three minus three multiply by x plus nine)
(x3-27)/(x3-3*x+9)
x3-27/x3-3*x+9
(x³-27)/(x³-3*x+9)
(x to the power of 3-27)/(x to the power of 3-3*x+9)
(x^3-27)/(x^3-3x+9)
(x3-27)/(x3-3x+9)
x3-27/x3-3x+9
x^3-27/x^3-3x+9
(x^3-27) divide by (x^3-3*x+9)
Similar expressions
(x^3-27)/(x^3-3*x-9)
(x^3-27)/(x^3+3*x+9)
(x^3+27)/(x^3-3*x+9)

How do you (x^3-27)/(x^3-3*x+9) in partial fractions?

You have entered [src]

   3        
  x  - 27   
------------
 3          
x  - 3*x + 9

$$\frac{x^{3} - 27}{\left(x^{3} - 3 x\right) + 9}$$

(x^3 - 27)/(x^3 - 3*x + 9)

General simplification [src]

         3  
  -27 + x   
------------
     3      
9 + x  - 3*x

$$\frac{x^{3} - 27}{x^{3} - 3 x + 9}$$

(-27 + x^3)/(9 + x^3 - 3*x)

Fraction decomposition [src]

1 + 3*(-12 + x)/(9 + x^3 - 3*x)

$$\frac{3 \left(x - 12\right)}{x^{3} - 3 x + 9} + 1$$

    3*(-12 + x) 
1 + ------------
         3      
    9 + x  - 3*x

Numerical answer [src]

(-27.0 + x^3)/(9.0 + x^3 - 3.0*x)

(-27.0 + x^3)/(9.0 + x^3 - 3.0*x)

Trigonometric part [src]

         3  
  -27 + x   
------------
     3      
9 + x  - 3*x

$$\frac{x^{3} - 27}{x^{3} - 3 x + 9}$$

(-27 + x^3)/(9 + x^3 - 3*x)

Combinatorics [src]

         /     2      \
(-3 + x)*\9 + x  + 3*x/
-----------------------
           3           
      9 + x  - 3*x

$$\frac{\left(x - 3\right) \left(x^{2} + 3 x + 9\right)}{x^{3} - 3 x + 9}$$

(-3 + x)*(9 + x^2 + 3*x)/(9 + x^3 - 3*x)

Assemble expression [src]

         3  
  -27 + x   
------------
     3      
9 + x  - 3*x

$$\frac{x^{3} - 27}{x^{3} - 3 x + 9}$$

(-27 + x^3)/(9 + x^3 - 3*x)

Rational denominator [src]

         3  
  -27 + x   
------------
     3      
9 + x  - 3*x

$$\frac{x^{3} - 27}{x^{3} - 3 x + 9}$$

(-27 + x^3)/(9 + x^3 - 3*x)

Common denominator [src]

     -36 + 3*x  
1 + ------------
         3      
    9 + x  - 3*x

$$\frac{3 x - 36}{x^{3} - 3 x + 9} + 1$$

1 + (-36 + 3*x)/(9 + x^3 - 3*x)

Combining rational expressions [src]

           3   
    -27 + x    
---------------
      /      2\
9 + x*\-3 + x /

$$\frac{x^{3} - 27}{x \left(x^{2} - 3\right) + 9}$$

(-27 + x^3)/(9 + x*(-3 + x^2))

Powers [src]

         3  
  -27 + x   
------------
     3      
9 + x  - 3*x

$$\frac{x^{3} - 27}{x^{3} - 3 x + 9}$$

(-27 + x^3)/(9 + x^3 - 3*x)