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

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

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

simplify

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

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

Solution steps

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

x - (x - 1) : 1

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

tan (θ) + cot (θ)

\frac{12 a ^{2} b}{3 a b ^{2}}

cos^{2} (t) + sin^{2} (t)

sin (x) + cos (x) cot (x)

\frac{sin ( x - 2 )}{sin ( x - 5 )}