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

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

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

simplify

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

- \frac{1}{x + 1}

Solution steps

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

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

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

Cancel

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

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

\frac{2}{3} (3 x + \frac{3}{5}) - 6 \frac{2}{5}

\frac{x ^{2} + 11 x + 28}{x + 4}

\frac{2}{cos ( x )}

(\frac{1}{4} - \frac{3}{5} n) - n

\frac{2 \cdot 35.6 + \frac{1}{2} \cdot 2.5 \cdot 3. 5 ^{2}}{2.5}