What is 1/(x+1)-2/((x+1)^2)+3/(x^2-1) ?

The solution to 1/(x+1)-2/((x+1)^2)+3/(x^2-1) is (x^2+x+4)/((x+1)^2(x-1))

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simplify 1/(x+1)-2/((x+1)^2)+3/(x^2-1)

simplify

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

\frac{x ^{2} + x + 4}{( x + 1 ) ^{2} ( x - 1 )}

Solution steps

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

(x + 1) (x - 1) - 2 (x - 1) + 3 (x + 1) : x^{2} + x + 4

= \frac{x ^{2} + x + 4}{( x + 1 ) ^{2} ( x - 1 )}

(a^{5})^{3}

\frac{13}{45} \cdot 3 \frac{6}{13} - \frac{4}{5}

(23 - 2 i)^{3}

- 0. 4^{2}

1 6^{- \frac{5}{2}}

What is 1/(x+1)-2/((x+1)^2)+3/(x^2-1) ?
The solution to 1/(x+1)-2/((x+1)^2)+3/(x^2-1) is (x^2+x+4)/((x+1)^2(x-1))