What is factor 1/(x^2-1)-2/((x+1)^2) ?

The solution to factor 1/(x^2-1)-2/((x+1)^2) is (-x+3)/((x+1)^2(x-1))

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

factor

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

\frac{- x + 3}{( x + 1 ) ^{2} ( x - 1 )}

Solution steps

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

Factor

x^{2} - 1 : (x + 1) (x - 1)

= \frac{1}{( x + 1 ) ( x - 1 )} - \frac{2}{( x + 1 ) ^{2}}

Least Common Multiplier of

(x + 1) (x - 1), (x + 1)^{2} : (x + 1)^{2} (x - 1)

Adjust Fractions based on the LCM

= \frac{x + 1}{( x + 1 ) ^{2} ( x - 1 )} - \frac{2 ( x - 1 )}{( x + 1 ) ^{2} ( x - 1 )}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{x + 1 - 2 ( x - 1 )}{( x + 1 ) ^{2} ( x - 1 )}

Expand

x + 1 - 2 (x - 1) : - x + 3

= \frac{- x + 3}{( x + 1 ) ^{2} ( x - 1 )}

\frac{25 - a ^{2}}{3 a - 15}

15 x^{2} - 25 x - 10

1098

9 - 3 i

25 x^{3} + 150 x^{2} - 9 x - 54

What is factor 1/(x^2-1)-2/((x+1)^2) ?
The solution to factor 1/(x^2-1)-2/((x+1)^2) is (-x+3)/((x+1)^2(x-1))