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

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

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

simplify

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

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

Solution steps

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

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

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

(2 x - 3) - (x - 6)

\frac{12 x ^{2}}{6 x ^{4} + 12 x ^{3}}

\frac{125}{5}

1.5625

\frac{1}{6 ^{- 3}}

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