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

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

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

simplify

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

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

Solution steps

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

Least Common Multiplier of

1 - x, 1 + x : (- x + 1) (x + 1)

Adjust Fractions based on the LCM

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

Simplify

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

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

x^{3} y^{4} + x y^{4}

\frac{x ^{4} - 9 x ^{2} + 4 x + 12}{( x + 1 )}

5 x^{2} + 35

40 \times \frac{1}{4}

- \frac{2}{3} + \frac{25}{36}