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

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

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

simplify

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

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

Solution steps

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

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

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

(1 + b)^{3}

(3 x + 4) (3 x + 4)

\frac{4}{22}

\frac{4}{40}

(3 y - 8) (- x + y)

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