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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)
Factor polynomial:
x^3-8
x^2+x-6
x^2+4
x^3+1
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 squared:
y^4+y^2+3
-y^4+y^2+14
y^4-y^2+15
y^4-y^2+3
Least common denominator:
y/(y+2)+(1/(4-y^2)-1/(4-4*y+y^2))/(2/(y-2)^2)
Identical expressions
y/(y+ two)+(one /(four -y^ two)- one /(four - four *y+y^ two))/(two /(y- two)^ two)
y divide by (y plus 2) plus (1 divide by (4 minus y squared ) minus 1 divide by (4 minus 4 multiply by y plus y squared )) divide by (2 divide by (y minus 2) squared )
y divide by (y plus two) plus (one divide by (four minus y to the power of two) minus one divide by (four minus four multiply by y plus y to the power of two)) divide by (two divide by (y minus two) to the power of two)
y/(y+2)+(1/(4-y2)-1/(4-4*y+y2))/(2/(y-2)2)
y/y+2+1/4-y2-1/4-4*y+y2/2/y-22
y/(y+2)+(1/(4-y²)-1/(4-4*y+y²))/(2/(y-2)²)
y/(y+2)+(1/(4-y to the power of 2)-1/(4-4*y+y to the power of 2))/(2/(y-2) to the power of 2)
y/(y+2)+(1/(4-y^2)-1/(4-4y+y^2))/(2/(y-2)^2)
y/(y+2)+(1/(4-y2)-1/(4-4y+y2))/(2/(y-2)2)
y/y+2+1/4-y2-1/4-4y+y2/2/y-22
y/y+2+1/4-y^2-1/4-4y+y^2/2/y-2^2
y divide by (y+2)+(1 divide by (4-y^2)-1 divide by (4-4*y+y^2)) divide by (2 divide by (y-2)^2)
Similar expressions
y/(y+2)+(1/(4-y^2)-1/(4+4*y+y^2))/(2/(y-2)^2)
y/(y+2)-(1/(4-y^2)-1/(4-4*y+y^2))/(2/(y-2)^2)
y/(y-2)+(1/(4-y^2)-1/(4-4*y+y^2))/(2/(y-2)^2)
y/(y+2)+(1/(4+y^2)-1/(4-4*y+y^2))/(2/(y-2)^2)
y/(y+2)+(1/(4-y^2)+1/(4-4*y+y^2))/(2/(y-2)^2)
y/(y+2)+(1/(4-y^2)-1/(4-4*y+y^2))/(2/(y+2)^2)
y/(y+2)+(1/(4-y^2)-1/(4-4*y-y^2))/(2/(y-2)^2)

Expression simplification/ Fraction Decomposition into the simple/ y/(y+2)+(1/(4-y^2)-1/(4-4*y+y^2))/(2/(y-2)^2)

How do you y/(y+2)+(1/(4-y^2)-1/(4-4*y+y^2))/(2/(y-2)^2) in partial fractions?

The solution

You have entered [src]

          1           1      
        ------ - ------------
             2              2
  y     4 - y    4 - 4*y + y 
----- + ---------------------
y + 2         /   2    \     
              |--------|     
              |       2|     
              \(y - 2) /

$$\frac{y}{y + 2} + \frac{- \frac{1}{y^{2} + \left(4 - 4 y\right)} + \frac{1}{4 - y^{2}}}{2 \frac{1}{\left(y - 2\right)^{2}}}$$

y/(y + 2) + (1/(4 - y^2) - 1/(4 - 4*y + y^2))/((2/(y - 2)^2))

Fraction decomposition [src]

$$0$$

General simplification [src]

$$0$$

Expand expression [src]

               2 /  1           1      \
        (y - 2) *|------ - ------------|
                 |     2              2|
  y              \4 - y    4 - 4*y + y /
----- + --------------------------------
y + 2                  2

$$\frac{y}{y + 2} + \frac{\left(y - 2\right)^{2} \left(- \frac{1}{y^{2} + \left(4 - 4 y\right)} + \frac{1}{4 - y^{2}}\right)}{2}$$

y/(y + 2) + (y - 2)^2*(1/(4 - y^2) - 1/(4 - 4*y + y^2))/2

Powers [src]

                2 /  1           1      \
        (-2 + y) *|------ - ------------|
                  |     2        2      |
  y               \4 - y    4 + y  - 4*y/
----- + ---------------------------------
2 + y                   2

$$\frac{y}{y + 2} + \frac{\left(y - 2\right)^{2} \left(- \frac{1}{y^{2} - 4 y + 4} + \frac{1}{4 - y^{2}}\right)}{2}$$

  y             2 /    1               1        \
----- + (-2 + y) *|---------- - ----------------|
2 + y             |  /     2\     /     2      \|
                  \2*\4 - y /   2*\4 + y  - 4*y//

$$\frac{y}{y + 2} + \left(y - 2\right)^{2} \left(- \frac{1}{2 \left(y^{2} - 4 y + 4\right)} + \frac{1}{2 \left(4 - y^{2}\right)}\right)$$

y/(2 + y) + (-2 + y)^2*(1/(2*(4 - y^2)) - 1/(2*(4 + y^2 - 4*y)))

Assemble expression [src]

                2 /  1           1      \
        (-2 + y) *|------ - ------------|
                  |     2        2      |
  y               \4 - y    4 + y  - 4*y/
----- + ---------------------------------
2 + y                   2

$$\frac{y}{y + 2} + \frac{\left(y - 2\right)^{2} \left(- \frac{1}{y^{2} - 4 y + 4} + \frac{1}{4 - y^{2}}\right)}{2}$$

y/(2 + y) + (-2 + y)^2*(1/(4 - y^2) - 1/(4 + y^2 - 4*y))/2

Numerical answer [src]

y/(2.0 + y) + 2.0*(-1 + 0.5*y)^2*(1/(4.0 - y^2) - 1/(4.0 + y^2 - 4.0*y))

y/(2.0 + y) + 2.0*(-1 + 0.5*y)^2*(1/(4.0 - y^2) - 1/(4.0 + y^2 - 4.0*y))

Rational denominator [src]

        2         /          2\       /     2\ /     2      \
(-2 + y) *(2 + y)*\-4*y + 2*y / + 2*y*\4 - y /*\4 + y  - 4*y/
-------------------------------------------------------------
                        /     2\ /     2      \              
              2*(2 + y)*\4 - y /*\4 + y  - 4*y/

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

((-2 + y)^2*(2 + y)*(-4*y + 2*y^2) + 2*y*(4 - y^2)*(4 + y^2 - 4*y))/(2*(2 + y)*(4 - y^2)*(4 + y^2 - 4*y))

Common denominator [src]

$$0$$

Combinatorics [src]

$$0$$

Combining rational expressions [src]

  /     2\ /     2      \           2         / 2      \
y*\4 - y /*\4 + y  - 4*y/ + (-2 + y) *(2 + y)*\y  - 2*y/
--------------------------------------------------------
                    /     2\ /     2      \             
            (2 + y)*\4 - y /*\4 + y  - 4*y/

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

(y*(4 - y^2)*(4 + y^2 - 4*y) + (-2 + y)^2*(2 + y)*(y^2 - 2*y))/((2 + y)*(4 - y^2)*(4 + y^2 - 4*y))

Trigonometric part [src]

                2 /  1           1      \
        (-2 + y) *|------ - ------------|
                  |     2        2      |
  y               \4 - y    4 + y  - 4*y/
----- + ---------------------------------
2 + y                   2

$$\frac{y}{y + 2} + \frac{\left(y - 2\right)^{2} \left(- \frac{1}{y^{2} - 4 y + 4} + \frac{1}{4 - y^{2}}\right)}{2}$$

y/(2 + y) + (-2 + y)^2*(1/(4 - y^2) - 1/(4 + y^2 - 4*y))/2

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Similar expressions

How do you y/(y+2)+(1/(4-y^2)-1/(4-4*y+y^2))/(2/(y-2)^2) in partial fractions?

The solution