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How do you in partial fractions?:
-x^2/(x-2)^2+2*x/(x-2)
(a^3+a)/(a^4+a)
1/(3*sqrt(1-x^2/9))
x^3/(x^8+1)
Factor polynomial:
x^6+27
x^4+4
x^3-x^5
x^2-y^2+x+y
Least common denominator:
(a/5+a/7)*a^2/4
(z/(z+6)*(z+6))-(z/(z-6)*(z+6))
z/(z+4)^2-z/z^2-16
(z+y*(x*z)/(z^2-x*y)+x*(z*y)/(z^2-x*y)-2*z*((x*z)/(z^2-x*y))*((z*y)/(z^2-x*y)))/(z^2-x*y)
Factor squared:
y^4-y^2+9
x^2+x+3
y^4-y^2+4
2*x^2+x*y-y^2
Least common denominator:
(x-1)*(1/(2*(x-1))-(x+1)/(2*(x-1)^2))/(x+1)
Identical expressions
(x- one)*(one /(two *(x- one))-(x+ one)/(two *(x- one)^ two))/(x+ one)
(x minus 1) multiply by (1 divide by (2 multiply by (x minus 1)) minus (x plus 1) divide by (2 multiply by (x minus 1) squared )) divide by (x plus 1)
(x minus one) multiply by (one divide by (two multiply by (x minus one)) minus (x plus one) divide by (two multiply by (x minus one) to the power of two)) divide by (x plus one)
(x-1)*(1/(2*(x-1))-(x+1)/(2*(x-1)2))/(x+1)
x-1*1/2*x-1-x+1/2*x-12/x+1
(x-1)*(1/(2*(x-1))-(x+1)/(2*(x-1)²))/(x+1)
(x-1)*(1/(2*(x-1))-(x+1)/(2*(x-1) to the power of 2))/(x+1)
(x-1)(1/(2(x-1))-(x+1)/(2(x-1)^2))/(x+1)
(x-1)(1/(2(x-1))-(x+1)/(2(x-1)2))/(x+1)
x-11/2x-1-x+1/2x-12/x+1
x-11/2x-1-x+1/2x-1^2/x+1
(x-1)*(1 divide by (2*(x-1))-(x+1) divide by (2*(x-1)^2)) divide by (x+1)
Similar expressions
(x-1)*(1/(2*(x-1))-(x-1)/(2*(x-1)^2))/(x+1)
(x-1)*(1/(2*(x-1))-(x+1)/(2*(x+1)^2))/(x+1)
(x-1)*(1/(2*(x-1))-(x+1)/(2*(x-1)^2))/(x-1)
(x+1)*(1/(2*(x-1))-(x+1)/(2*(x-1)^2))/(x+1)
(x-1)*(1/(2*(x-1))+(x+1)/(2*(x-1)^2))/(x+1)
(x-1)*(1/(2*(x+1))-(x+1)/(2*(x-1)^2))/(x+1)

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

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

The solution

You have entered [src]

        /    1         x + 1   \
(x - 1)*|--------- - ----------|
        |2*(x - 1)            2|
        \            2*(x - 1) /
--------------------------------
             x + 1

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

((x - 1)*(1/(2*(x - 1)) - (x + 1)/(2*(x - 1)^2)))/(x + 1)

Fraction decomposition [src]

1/(2*(1 + x)) - 1/(2*(-1 + x))

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

    1           1     
--------- - ----------
2*(1 + x)   2*(-1 + x)

General simplification [src]

  -1   
-------
      2
-1 + x

$$- \frac{1}{x^{2} - 1}$$

-1/(-1 + x^2)

Expand expression [src]

        /    1         x + 1   \
(x - 1)*|--------- - ----------|
        |2*(x - 1)            2|
        \            2*(x - 1) /
--------------------------------
             x + 1

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

(x - 1)*(1/(2*(x - 1)) - (x + 1)/(2*(x - 1)^2))/(x + 1)

Combining rational expressions [src]

      -1        
----------------
(1 + x)*(-1 + x)

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

-1/((1 + x)*(-1 + x))

Numerical answer [src]

(-1.0 + x)*(1/(-2.0 + 2.0*x) - 0.5*(1.0 + x)/(-1.0 + x)^2)/(1.0 + x)

(-1.0 + x)*(1/(-2.0 + 2.0*x) - 0.5*(1.0 + x)/(-1.0 + x)^2)/(1.0 + x)

Trigonometric part [src]

         /   1          1 + x   \
(-1 + x)*|-------- - -----------|
         |-2 + 2*x             2|
         \           2*(-1 + x) /
---------------------------------
              1 + x

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

(-1 + x)*(1/(-2 + 2*x) - (1 + x)/(2*(-1 + x)^2))/(1 + x)

Common denominator [src]

  -1   
-------
      2
-1 + x

$$- \frac{1}{x^{2} - 1}$$

-1/(-1 + x^2)

Powers [src]

         /   1          1 + x   \
(-1 + x)*|-------- - -----------|
         |-2 + 2*x             2|
         \           2*(-1 + x) /
---------------------------------
              1 + x

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

         /              1   x \
         |            - - - - |
         |   1          2   2 |
(-1 + x)*|-------- + ---------|
         |-2 + 2*x           2|
         \           (-1 + x) /
-------------------------------
             1 + x

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

(-1 + x)*(1/(-2 + 2*x) + (-1/2 - x/2)/(-1 + x)^2)/(1 + x)

Combinatorics [src]

      -1        
----------------
(1 + x)*(-1 + x)

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

-1/((1 + x)*(-1 + x))

Rational denominator [src]

          2                      
2*(-1 + x)  + (-1 - x)*(-2 + 2*x)
---------------------------------
  2*(1 + x)*(-1 + x)*(-2 + 2*x)

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

(2*(-1 + x)^2 + (-1 - x)*(-2 + 2*x))/(2*(1 + x)*(-1 + x)*(-2 + 2*x))

Assemble expression [src]

         /   1          1 + x   \
(-1 + x)*|-------- - -----------|
         |-2 + 2*x             2|
         \           2*(-1 + x) /
---------------------------------
              1 + x

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

(-1 + x)*(1/(-2 + 2*x) - (1 + x)/(2*(-1 + x)^2))/(1 + x)

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Identical expressions

Similar expressions

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

The solution

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