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How to use it?
How do you in partial fractions?:
(a^4-10*a^2+169)/(a^2+6*a+13)
((3*x+2)^4+12*(3*x+2)^3*(x-1))/(3*x-2)^4-12*(3*x+2)^4*(x-1)/(3*x-2)^5
((x+3)/(x-1))^2+14(x^2-9)/(x^2-1)-15((x-3)/(x+1))^2
((x+12)/(x^(3)-9x))/(((x-3)/(2x^2+5x-3))-(9/(9-x^2)))
Factor polynomial:
-x^7+x^6/4+9*x^5/8-9*x^4/32-x^3/8+x^2/32
x^7+4*x^6+4*x^5+2*x^4+4*x^3+3*x^2+3*x+4
x^7-4*x^5+6*x^3-4*x
x^7-3*x^6+8*x^2
Least common denominator:
((u^2-2*u+4)/(4*u^2-1)*(2*u^2+u)/(u^3+8)-(u+2/2*u^2-u))/7/(u^2+2*u)-(10*u+1)/(7-14*u)
t/(t-7)-7/(7-t)
sqrt((x-3)/(x+3))*(x+3)*(1/(2*(x+3))-(x-3)/(2*(x+3)^2))/(x-3)
sqrt(x)*(3*x^2-1/(2*x*sqrt(x)))+(x^3+1/(sqrt(x)))/(2*sqrt(x))
Factor squared:
-y^2-7*y*x-x^2
-y^2-7*y*x-15*x^2
-y^2+7*y*x+7*x^2
y^2-7*y*x+5*x^2
Identical expressions
((x+ three)/(x- one))^ two + fourteen (x^ two - nine)/(x^ two - one)- fifteen ((x- three)/(x+ one))^ two
((x plus 3) divide by (x minus 1)) squared plus 14(x squared minus 9) divide by (x squared minus 1) minus 15((x minus 3) divide by (x plus 1)) squared
((x plus three) divide by (x minus one)) to the power of two plus fourteen (x to the power of two minus nine) divide by (x to the power of two minus one) minus fifteen ((x minus three) divide by (x plus one)) to the power of two
((x+3)/(x-1))2+14(x2-9)/(x2-1)-15((x-3)/(x+1))2
x+3/x-12+14x2-9/x2-1-15x-3/x+12
((x+3)/(x-1))²+14(x²-9)/(x²-1)-15((x-3)/(x+1))²
((x+3)/(x-1)) to the power of 2+14(x to the power of 2-9)/(x to the power of 2-1)-15((x-3)/(x+1)) to the power of 2
x+3/x-1^2+14x^2-9/x^2-1-15x-3/x+1^2
((x+3) divide by (x-1))^2+14(x^2-9) divide by (x^2-1)-15((x-3) divide by (x+1))^2
Similar expressions
((x+3)/(x-1))^2+14(x^2-9)/(x^2-1)-15((x+3)/(x+1))^2
((x+3)/(x-1))^2-14(x^2-9)/(x^2-1)-15((x-3)/(x+1))^2
((x+3)/(x-1))^2+14(x^2-9)/(x^2+1)-15((x-3)/(x+1))^2
((x+3)/(x+1))^2+14(x^2-9)/(x^2-1)-15((x-3)/(x+1))^2
((x+3)/(x-1))^2+14(x^2-9)/(x^2-1)+15((x-3)/(x+1))^2
((x+3)/(x-1))^2+14(x^2+9)/(x^2-1)-15((x-3)/(x+1))^2
((x-3)/(x-1))^2+14(x^2-9)/(x^2-1)-15((x-3)/(x+1))^2
((x+3)/(x-1))^2+14(x^2-9)/(x^2-1)-15((x-3)/(x-1))^2

Expression simplification/ Fraction Decomposition into the simple/ ((x+3)/(x-1))^2+14(x^2-9)/(x^2-1)-15((x-3)/(x+1))^2

How do you ((x+3)/(x-1))^2+14(x^2-9)/(x^2-1)-15((x-3)/(x+1))^2 in partial fractions?

The solution

You have entered [src]

       2      / 2    \             2
/x + 3\    14*\x  - 9/      /x - 3\ 
|-----|  + ----------- - 15*|-----| 
\x - 1/        2            \x + 1/ 
              x  - 1

$$- 15 \left(\frac{x - 3}{x + 1}\right)^{2} + \left(\left(\frac{x + 3}{x - 1}\right)^{2} + \frac{14 \left(x^{2} - 9\right)}{x^{2} - 1}\right)$$

((x + 3)/(x - 1))^2 + (14*(x^2 - 9))/(x^2 - 1) - 15*(x - 3)^2/(x + 1)^2

General simplification [src]

     /             2\
64*x*\6 - 7*x + 2*x /
---------------------
         4      2    
    1 + x  - 2*x

$$\frac{64 x \left(2 x^{2} - 7 x + 6\right)}{x^{4} - 2 x^{2} + 1}$$

64*x*(6 - 7*x + 2*x^2)/(1 + x^4 - 2*x^2)

Fraction decomposition [src]

-240/(1 + x)^2 - 48/(-1 + x) + 16/(-1 + x)^2 + 176/(1 + x)

$$\frac{176}{x + 1} - \frac{240}{\left(x + 1\right)^{2}} - \frac{48}{x - 1} + \frac{16}{\left(x - 1\right)^{2}}$$

    240        48         16       176 
- -------- - ------ + --------- + -----
         2   -1 + x           2   1 + x
  (1 + x)             (-1 + x)

Expand expression [src]

       2      / 2    \             2
(x + 3)    14*\x  - 9/   15*(x - 3) 
-------- + ----------- - -----------
       2       2                  2 
(x - 1)       x  - 1       (x + 1)

$$- \frac{15 \left(x - 3\right)^{2}}{\left(x + 1\right)^{2}} + \frac{14 \left(x^{2} - 9\right)}{x^{2} - 1} + \frac{\left(x + 3\right)^{2}}{\left(x - 1\right)^{2}}$$

(x + 3)^2/(x - 1)^2 + (14*(x^2 - 9))/(x^2 - 1) - 15*(x - 3)^2/(x + 1)^2

Rational denominator [src]

       2 /        2 /           2\          2 /      2\\              2         2 /      2\
(1 + x) *\(-1 + x) *\-126 + 14*x / + (3 + x) *\-1 + x // - 15*(-1 + x) *(-3 + x) *\-1 + x /
-------------------------------------------------------------------------------------------
                                       2         2 /      2\                               
                                (1 + x) *(-1 + x) *\-1 + x /

$$\frac{- 15 \left(x - 3\right)^{2} \left(x - 1\right)^{2} \left(x^{2} - 1\right) + \left(x + 1\right)^{2} \left(\left(x - 1\right)^{2} \left(14 x^{2} - 126\right) + \left(x + 3\right)^{2} \left(x^{2} - 1\right)\right)}{\left(x - 1\right)^{2} \left(x + 1\right)^{2} \left(x^{2} - 1\right)}$$

((1 + x)^2*((-1 + x)^2*(-126 + 14*x^2) + (3 + x)^2*(-1 + x^2)) - 15*(-1 + x)^2*(-3 + x)^2*(-1 + x^2))/((1 + x)^2*(-1 + x)^2*(-1 + x^2))

Assemble expression [src]

        2              2              2
 (3 + x)    -126 + 14*x    15*(-3 + x) 
--------- + ------------ - ------------
        2           2               2  
(-1 + x)      -1 + x         (1 + x)

$$- \frac{15 \left(x - 3\right)^{2}}{\left(x + 1\right)^{2}} + \frac{14 x^{2} - 126}{x^{2} - 1} + \frac{\left(x + 3\right)^{2}}{\left(x - 1\right)^{2}}$$

(3 + x)^2/(-1 + x)^2 + (-126 + 14*x^2)/(-1 + x^2) - 15*(-3 + x)^2/(1 + x)^2

Trigonometric part [src]

        2              2              2
 (3 + x)    -126 + 14*x    15*(-3 + x) 
--------- + ------------ - ------------
        2           2               2  
(-1 + x)      -1 + x         (1 + x)

$$- \frac{15 \left(x - 3\right)^{2}}{\left(x + 1\right)^{2}} + \frac{14 x^{2} - 126}{x^{2} - 1} + \frac{\left(x + 3\right)^{2}}{\left(x - 1\right)^{2}}$$

(3 + x)^2/(-1 + x)^2 + (-126 + 14*x^2)/(-1 + x^2) - 15*(-3 + x)^2/(1 + x)^2

Combining rational expressions [src]

       2 /       2 /      2\              2 /      2\\              2         2 /      2\
(1 + x) *\(3 + x) *\-1 + x / + 14*(-1 + x) *\-9 + x // - 15*(-1 + x) *(-3 + x) *\-1 + x /
-----------------------------------------------------------------------------------------
                                      2         2 /      2\                              
                               (1 + x) *(-1 + x) *\-1 + x /

$$\frac{- 15 \left(x - 3\right)^{2} \left(x - 1\right)^{2} \left(x^{2} - 1\right) + \left(x + 1\right)^{2} \left(14 \left(x - 1\right)^{2} \left(x^{2} - 9\right) + \left(x + 3\right)^{2} \left(x^{2} - 1\right)\right)}{\left(x - 1\right)^{2} \left(x + 1\right)^{2} \left(x^{2} - 1\right)}$$

((1 + x)^2*((3 + x)^2*(-1 + x^2) + 14*(-1 + x)^2*(-9 + x^2)) - 15*(-1 + x)^2*(-3 + x)^2*(-1 + x^2))/((1 + x)^2*(-1 + x)^2*(-1 + x^2))

Numerical answer [src]

(-126.0 + 14.0*x^2)/(-1.0 + x^2) + 9.0*(1 + 0.333333333333333*x)^2/(-1.0 + x)^2 - 135.0*(-1 + 0.333333333333333*x)^2/(1.0 + x)^2

(-126.0 + 14.0*x^2)/(-1.0 + x^2) + 9.0*(1 + 0.333333333333333*x)^2/(-1.0 + x)^2 - 135.0*(-1 + 0.333333333333333*x)^2/(1.0 + x)^2

Common denominator [src]

       2        3        
- 448*x  + 128*x  + 384*x
-------------------------
           4      2      
      1 + x  - 2*x

$$\frac{128 x^{3} - 448 x^{2} + 384 x}{x^{4} - 2 x^{2} + 1}$$

(-448*x^2 + 128*x^3 + 384*x)/(1 + x^4 - 2*x^2)

Powers [src]

        2              2              2
 (3 + x)    -126 + 14*x    15*(-3 + x) 
--------- + ------------ - ------------
        2           2               2  
(-1 + x)      -1 + x         (1 + x)

$$- \frac{15 \left(x - 3\right)^{2}}{\left(x + 1\right)^{2}} + \frac{14 x^{2} - 126}{x^{2} - 1} + \frac{\left(x + 3\right)^{2}}{\left(x - 1\right)^{2}}$$

(3 + x)^2/(-1 + x)^2 + (-126 + 14*x^2)/(-1 + x^2) - 15*(-3 + x)^2/(1 + x)^2

Combinatorics [src]

64*x*(-3 + 2*x)*(-2 + x)
------------------------
          2         2   
   (1 + x) *(-1 + x)

$$\frac{64 x \left(x - 2\right) \left(2 x - 3\right)}{\left(x - 1\right)^{2} \left(x + 1\right)^{2}}$$

64*x*(-3 + 2*x)*(-2 + x)/((1 + x)^2*(-1 + x)^2)

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Identical expressions

Similar expressions

How do you ((x+3)/(x-1))^2+14(x^2-9)/(x^2-1)-15((x-3)/(x+1))^2 in partial fractions?

The solution