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

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

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

simplify

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

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

Solution steps

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

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

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

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

1 - (- 8)

(4 + ((2 - 5)^{2} - 4 (7 - 5)^{3} + 2 (\frac{15}{3}))) - 16

- 4 - - 25

4 \frac{3}{5} + 7 \frac{1}{2}

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