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How do you in partial fractions?:
x^2-9/(x+3)^2
(4x-1)/(x^2-4x+8)
1/(x^4+x^2)
((x*x)*x-15*x)*(-2*x/((x*x)*x-15*x)+(5-x*x)*(15-x^2-2*x^2)/((x*x)*x-15*x)^2)/(4*(5-x*x))
Factor polynomial:
y^2+8*y+16
y^2+4*y-60
y^2-4*y-42
y^2+4*y^2
Least common denominator:
(x+3/(6*x-30))*(450/(x^2+3*x))
((x^3+6*x^2+11*x+6)/(-6))+((-x^3-9*x^2-26*x-24)/6)
x^2*y+16/(y-1)*(x-4)-16*y+x^2/x*y-x-4*y+4
(x2-x1)*x1-(c/a-x1*(x1+x2)/2)
Factor squared:
-y^2-y*q-4*q^2
y^2+y*q+4*q^2
-y^2+y*x+2*x^2
y^2-y*t-6*t^2
Least common denominator:
((x*x)*x-15*x)*(-2*x/((x*x)*x-15*x)+(5-x*x)*(15-x^2-2*x^2)/((x*x)*x-15*x)^2)/(4*(5-x*x))
Identical expressions
((x*x)*x- fifteen *x)*(- two *x/((x*x)*x- fifteen *x)+(five -x*x)*(fifteen -x^ two - two *x^ two)/((x*x)*x- fifteen *x)^ two)/(four *(five -x*x))
((x multiply by x) multiply by x minus 15 multiply by x) multiply by ( minus 2 multiply by x divide by ((x multiply by x) multiply by x minus 15 multiply by x) plus (5 minus x multiply by x) multiply by (15 minus x squared minus 2 multiply by x squared ) divide by ((x multiply by x) multiply by x minus 15 multiply by x) squared ) divide by (4 multiply by (5 minus x multiply by x))
((x multiply by x) multiply by x minus fifteen multiply by x) multiply by ( minus two multiply by x divide by ((x multiply by x) multiply by x minus fifteen multiply by x) plus (five minus x multiply by x) multiply by (fifteen minus x to the power of two minus two multiply by x to the power of two) divide by ((x multiply by x) multiply by x minus fifteen multiply by x) to the power of two) divide by (four multiply by (five minus x multiply by x))
((x*x)*x-15*x)*(-2*x/((x*x)*x-15*x)+(5-x*x)*(15-x2-2*x2)/((x*x)*x-15*x)2)/(4*(5-x*x))
x*x*x-15*x*-2*x/x*x*x-15*x+5-x*x*15-x2-2*x2/x*x*x-15*x2/4*5-x*x
((x*x)*x-15*x)*(-2*x/((x*x)*x-15*x)+(5-x*x)*(15-x²-2*x²)/((x*x)*x-15*x)²)/(4*(5-x*x))
((x*x)*x-15*x)*(-2*x/((x*x)*x-15*x)+(5-x*x)*(15-x to the power of 2-2*x to the power of 2)/((x*x)*x-15*x) to the power of 2)/(4*(5-x*x))
((xx)x-15x)(-2x/((xx)x-15x)+(5-xx)(15-x^2-2x^2)/((xx)x-15x)^2)/(4(5-xx))
((xx)x-15x)(-2x/((xx)x-15x)+(5-xx)(15-x2-2x2)/((xx)x-15x)2)/(4(5-xx))
xxx-15x-2x/xxx-15x+5-xx15-x2-2x2/xxx-15x2/45-xx
xxx-15x-2x/xxx-15x+5-xx15-x^2-2x^2/xxx-15x^2/45-xx
((x*x)*x-15*x)*(-2*x divide by ((x*x)*x-15*x)+(5-x*x)*(15-x^2-2*x^2) divide by ((x*x)*x-15*x)^2) divide by (4*(5-x*x))
Similar expressions
((x*x)*x-15*x)*(-2*x/((x*x)*x-15*x)+(5-x*x)*(15-x^2+2*x^2)/((x*x)*x-15*x)^2)/(4*(5-x*x))
((x*x)*x-15*x)*(2*x/((x*x)*x-15*x)+(5-x*x)*(15-x^2-2*x^2)/((x*x)*x-15*x)^2)/(4*(5-x*x))
((x*x)*x-15*x)*(-2*x/((x*x)*x+15*x)+(5-x*x)*(15-x^2-2*x^2)/((x*x)*x-15*x)^2)/(4*(5-x*x))
((x*x)*x-15*x)*(-2*x/((x*x)*x-15*x)+(5-x*x)*(15-x^2-2*x^2)/((x*x)*x+15*x)^2)/(4*(5-x*x))
((x*x)*x-15*x)*(-2*x/((x*x)*x-15*x)+(5+x*x)*(15-x^2-2*x^2)/((x*x)*x-15*x)^2)/(4*(5-x*x))
((x*x)*x-15*x)*(-2*x/((x*x)*x-15*x)+(5-x*x)*(15-x^2-2*x^2)/((x*x)*x-15*x)^2)/(4*(5+x*x))
((x*x)*x-15*x)*(-2*x/((x*x)*x-15*x)+(5-x*x)*(15+x^2-2*x^2)/((x*x)*x-15*x)^2)/(4*(5-x*x))
((x*x)*x+15*x)*(-2*x/((x*x)*x-15*x)+(5-x*x)*(15-x^2-2*x^2)/((x*x)*x-15*x)^2)/(4*(5-x*x))
((x*x)*x-15*x)*(-2*x/((x*x)*x-15*x)-(5-x*x)*(15-x^2-2*x^2)/((x*x)*x-15*x)^2)/(4*(5-x*x))

Expression simplification/ Fraction Decomposition into the simple/ ((x*x)*x-15*x)*(-2*x/((x*x)*x-15*x)+(5-x*x)*(15-x^2-2*x^2)/((x*x)*x-15*x)^2)/(4*(5-x*x))

How do you ((xx)x-15x)(-2x/((xx)x-15x)+(5-xx)(15-x^2-2x^2)/((xx)x-15x)^2)/(4(5-xx)) in partial fractions?

The solution

You have entered [src]

               /                         /      2      2\\
               |    -2*x       (5 - x*x)*\15 - x  - 2*x /|
(x*x*x - 15*x)*|------------ + --------------------------|
               |x*x*x - 15*x                      2      |
               \                    (x*x*x - 15*x)       /
----------------------------------------------------------
                       4*(5 - x*x)

$$\frac{\left(\frac{\left(-1\right) 2 x}{x x x - 15 x} + \frac{\left(- 2 x^{2} + \left(15 - x^{2}\right)\right) \left(- x x + 5\right)}{\left(x x x - 15 x\right)^{2}}\right) \left(x x x - 15 x\right)}{4 \left(- x x + 5\right)}$$

(((x*x)*x - 15*x)*((-2*x)/((x*x)*x - 15*x) + ((5 - x*x)*(15 - x^2 - 2*x^2))/((x*x)*x - 15*x)^2))/((4*(5 - x*x)))

General simplification [src]

      /      4\      
     -\75 + x /      
---------------------
    /      4       2\
4*x*\75 + x  - 20*x /

$$- \frac{x^{4} + 75}{4 x \left(x^{4} - 20 x^{2} + 75\right)}$$

-(75 + x^4)/(4*x*(75 + x^4 - 20*x^2))

Fraction decomposition [src]

-1/(4*x) + x/(2*(-5 + x^2)) - x/(2*(-15 + x^2))

$$\frac{x}{2 \left(x^{2} - 5\right)} - \frac{x}{2 \left(x^{2} - 15\right)} - \frac{1}{4 x}$$

   1         x             x      
- --- + ----------- - ------------
  4*x     /      2\     /       2\
        2*\-5 + x /   2*\-15 + x /

Numerical answer [src]

(x^3 - 15.0*x)*(-2.0*x/(x^3 - 15.0*x) + 0.00444444444444444*(5.0 - x^2)*(15.0 - 3.0*x^2)/(-x + 0.0666666666666667*x^3)^2)/(20.0 - 4.0*x^2)

(x^3 - 15.0*x)*(-2.0*x/(x^3 - 15.0*x) + 0.00444444444444444*(5.0 - x^2)*(15.0 - 3.0*x^2)/(-x + 0.0666666666666667*x^3)^2)/(20.0 - 4.0*x^2)

Rational denominator [src]

                 2                                   
      / 3       \    /     2\ /        2\ / 3       \
- 2*x*\x  - 15*x/  + \5 - x /*\15 - 3*x /*\x  - 15*x/
-----------------------------------------------------
                                      2              
               /        2\ / 3       \               
               \20 - 4*x /*\x  - 15*x/

$$\frac{- 2 x \left(x^{3} - 15 x\right)^{2} + \left(5 - x^{2}\right) \left(15 - 3 x^{2}\right) \left(x^{3} - 15 x\right)}{\left(20 - 4 x^{2}\right) \left(x^{3} - 15 x\right)^{2}}$$

(-2*x*(x^3 - 15*x)^2 + (5 - x^2)*(15 - 3*x^2)*(x^3 - 15*x))/((20 - 4*x^2)*(x^3 - 15*x)^2)

Assemble expression [src]

            /              /     2\ /        2\\
/ 3       \ |     2*x      \5 - x /*\15 - 3*x /|
\x  - 15*x/*|- --------- + --------------------|
            |   3                         2    |
            |  x  - 15*x       / 3       \     |
            \                  \x  - 15*x/     /
------------------------------------------------
                           2                    
                   20 - 4*x

$$\frac{\left(x^{3} - 15 x\right) \left(- \frac{2 x}{x^{3} - 15 x} + \frac{\left(5 - x^{2}\right) \left(15 - 3 x^{2}\right)}{\left(x^{3} - 15 x\right)^{2}}\right)}{20 - 4 x^{2}}$$

(x^3 - 15*x)*(-2*x/(x^3 - 15*x) + (5 - x^2)*(15 - 3*x^2)/(x^3 - 15*x)^2)/(20 - 4*x^2)

Combining rational expressions [src]

          2                  
  /     2\       2 /       2\
3*\5 - x /  - 2*x *\-15 + x /
-----------------------------
     /       2\ /        2\  
   x*\-15 + x /*\20 - 4*x /

$$\frac{- 2 x^{2} \left(x^{2} - 15\right) + 3 \left(5 - x^{2}\right)^{2}}{x \left(20 - 4 x^{2}\right) \left(x^{2} - 15\right)}$$

(3*(5 - x^2)^2 - 2*x^2*(-15 + x^2))/(x*(-15 + x^2)*(20 - 4*x^2))

Combinatorics [src]

       /      4\        
      -\75 + x /        
------------------------
    /       2\ /      2\
4*x*\-15 + x /*\-5 + x /

$$- \frac{x^{4} + 75}{4 x \left(x^{2} - 15\right) \left(x^{2} - 5\right)}$$

-(75 + x^4)/(4*x*(-15 + x^2)*(-5 + x^2))

Powers [src]

            /              /     2\ /        2\\
/ 3       \ |     2*x      \5 - x /*\15 - 3*x /|
\x  - 15*x/*|- --------- + --------------------|
            |   3                         2    |
            |  x  - 15*x       / 3       \     |
            \                  \x  - 15*x/     /
------------------------------------------------
                           2                    
                   20 - 4*x

$$\frac{\left(x^{3} - 15 x\right) \left(- \frac{2 x}{x^{3} - 15 x} + \frac{\left(5 - x^{2}\right) \left(15 - 3 x^{2}\right)}{\left(x^{3} - 15 x\right)^{2}}\right)}{20 - 4 x^{2}}$$

(x^3 - 15*x)*(-2*x/(x^3 - 15*x) + (5 - x^2)*(15 - 3*x^2)/(x^3 - 15*x)^2)/(20 - 4*x^2)

Trigonometric part [src]

            /              /     2\ /        2\\
/ 3       \ |     2*x      \5 - x /*\15 - 3*x /|
\x  - 15*x/*|- --------- + --------------------|
            |   3                         2    |
            |  x  - 15*x       / 3       \     |
            \                  \x  - 15*x/     /
------------------------------------------------
                           2                    
                   20 - 4*x

$$\frac{\left(x^{3} - 15 x\right) \left(- \frac{2 x}{x^{3} - 15 x} + \frac{\left(5 - x^{2}\right) \left(15 - 3 x^{2}\right)}{\left(x^{3} - 15 x\right)^{2}}\right)}{20 - 4 x^{2}}$$

(x^3 - 15*x)*(-2*x/(x^3 - 15*x) + (5 - x^2)*(15 - 3*x^2)/(x^3 - 15*x)^2)/(20 - 4*x^2)

Common denominator [src]

      /      4\       
     -\75 + x /       
----------------------
      3      5        
- 80*x  + 4*x  + 300*x

$$- \frac{x^{4} + 75}{4 x^{5} - 80 x^{3} + 300 x}$$

-(75 + x^4)/(-80*x^3 + 4*x^5 + 300*x)

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How to use it?

Identical expressions

Similar expressions

How do you ((x*x)*x-15*x)*(-2*x/((x*x)*x-15*x)+(5-x*x)*(15-x^2-2*x^2)/((x*x)*x-15*x)^2)/(4*(5-x*x)) in partial fractions?

The solution

How do you ((xx)x-15x)(-2x/((xx)x-15x)+(5-xx)(15-x^2-2x^2)/((xx)x-15x)^2)/(4(5-xx)) in partial fractions?