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How do you in partial fractions?:
2*x/(x^2+1)-2*x*(x^2-1)/(x^2+1)^2
(((y-y)/(3*y-3))+(1/(y-1)))/((y+1)/3)+(2/(y^2-1))
y*(y+((1/(x+(x^2+y^2)^(1/2))*(1+(2*x/(2*(x^2+y^2)^(1/2)))))))-(y/(x^2+y^2)^(1/2))
((25*x^2)-1)/((25*x^2)-10*x+1)
Factor polynomial:
x^3-1
x^7+1
c^5+1
x^2-4
Least common denominator:
(z/b-b/z)*6*z*b/(z+b)
(((z)/(b))-((b)/(z)))*((4*z*b)/(z+b))
(z/8+z/3)/z^2
(z-6*z/z+3)/z-3/z+3
Factor squared:
y^4+y^2-1
-y^4+9*y^2+5
y^4-9*y^2+4
y^4+9*y^2+3
Least common denominator:
(((y-y)/(3*y-3))+(1/(y-1)))/((y+1)/3)+(2/(y^2-1))
Identical expressions
(((y-y)/(three *y- three))+(one /(y- one)))/((y+ one)/ three)+(two /(y^ two - one))
(((y minus y) divide by (3 multiply by y minus 3)) plus (1 divide by (y minus 1))) divide by ((y plus 1) divide by 3) plus (2 divide by (y squared minus 1))
(((y minus y) divide by (three multiply by y minus three)) plus (one divide by (y minus one))) divide by ((y plus one) divide by three) plus (two divide by (y to the power of two minus one))
(((y-y)/(3*y-3))+(1/(y-1)))/((y+1)/3)+(2/(y2-1))
y-y/3*y-3+1/y-1/y+1/3+2/y2-1
(((y-y)/(3*y-3))+(1/(y-1)))/((y+1)/3)+(2/(y²-1))
(((y-y)/(3*y-3))+(1/(y-1)))/((y+1)/3)+(2/(y to the power of 2-1))
(((y-y)/(3y-3))+(1/(y-1)))/((y+1)/3)+(2/(y^2-1))
(((y-y)/(3y-3))+(1/(y-1)))/((y+1)/3)+(2/(y2-1))
y-y/3y-3+1/y-1/y+1/3+2/y2-1
y-y/3y-3+1/y-1/y+1/3+2/y^2-1
(((y-y) divide by (3*y-3))+(1 divide by (y-1))) divide by ((y+1) divide by 3)+(2 divide by (y^2-1))
Similar expressions
(((y-y)/(3*y-3))+(1/(y+1)))/((y+1)/3)+(2/(y^2-1))
(((y-y)/(3*y-3))-(1/(y-1)))/((y+1)/3)+(2/(y^2-1))
(((y+y)/(3*y-3))+(1/(y-1)))/((y+1)/3)+(2/(y^2-1))
(((y-y)/(3*y-3))+(1/(y-1)))/((y+1)/3)+(2/(y^2+1))
(((y-y)/(3*y-3))+(1/(y-1)))/((y+1)/3)-(2/(y^2-1))
(((y-y)/(3*y+3))+(1/(y-1)))/((y+1)/3)+(2/(y^2-1))
(((y-y)/(3*y-3))+(1/(y-1)))/((y-1)/3)+(2/(y^2-1))

Expression simplification/ Fraction Decomposition into the simple/ (((y-y)/(3*y-3))+(1/(y-1)))/((y+1)/3)+(2/(y^2-1))

How do you (((y-y)/(3*y-3))+(1/(y-1)))/((y+1)/3)+(2/(y^2-1)) in partial fractions?

The solution

You have entered [src]

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

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

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

Fraction decomposition [src]

-5/(2*(1 + y)) + 5/(2*(-1 + y))

$$- \frac{5}{2 \left(y + 1\right)} + \frac{5}{2 \left(y - 1\right)}$$

      5           5     
- --------- + ----------
  2*(1 + y)   2*(-1 + y)

General simplification [src]

   5   
-------
      2
-1 + y

$$\frac{5}{y^{2} - 1}$$

5/(-1 + y^2)

Rational denominator [src]

/      2\                                           
\-1 + y /*(-9 + 9*y) + 2*(1 + y)*(-1 + y)*(-3 + 3*y)
----------------------------------------------------
                        /      2\                   
       (1 + y)*(-1 + y)*\-1 + y /*(-3 + 3*y)

$$\frac{2 \left(y - 1\right) \left(y + 1\right) \left(3 y - 3\right) + \left(9 y - 9\right) \left(y^{2} - 1\right)}{\left(y - 1\right) \left(y + 1\right) \left(3 y - 3\right) \left(y^{2} - 1\right)}$$

((-1 + y^2)*(-9 + 9*y) + 2*(1 + y)*(-1 + y)*(-3 + 3*y))/((1 + y)*(-1 + y)*(-1 + y^2)*(-3 + 3*y))

Common denominator [src]

   5   
-------
      2
-1 + y

$$\frac{5}{y^{2} - 1}$$

5/(-1 + y^2)

Powers [src]

   2             1        
------- + ----------------
      2            /1   y\
-1 + y    (-1 + y)*|- + -|
                   \3   3/

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

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

Trigonometric part [src]

   2             1        
------- + ----------------
      2            /1   y\
-1 + y    (-1 + y)*|- + -|
                   \3   3/

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

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

Expand expression [src]

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

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

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

Combinatorics [src]

       5        
----------------
(1 + y)*(-1 + y)

$$\frac{5}{\left(y - 1\right) \left(y + 1\right)}$$

5/((1 + y)*(-1 + y))

Assemble expression [src]

   2             1        
------- + ----------------
      2            /1   y\
-1 + y    (-1 + y)*|- + -|
                   \3   3/

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

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

Combining rational expressions [src]

        2                     
-3 + 3*y  + 2*(1 + y)*(-1 + y)
------------------------------
                   /      2\  
  (1 + y)*(-1 + y)*\-1 + y /

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

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

Numerical answer [src]

2.0/(-1.0 + y^2) + 1/((0.333333333333333 + 0.333333333333333*y)*(-1.0 + y))

2.0/(-1.0 + y^2) + 1/((0.333333333333333 + 0.333333333333333*y)*(-1.0 + y))

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Similar expressions

How do you (((y-y)/(3*y-3))+(1/(y-1)))/((y+1)/3)+(2/(y^2-1)) in partial fractions?

The solution