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

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

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

simplify

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

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

Solution steps

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Simplify

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

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

(3 x + 2 y - 4) + (2 x - 3 y + 9) + (4 x + 5 y + 1)

\frac{310}{180}

\frac{41}{12}

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

(x^{2} - x - 1) (- 3 x^{2} - 2 x - 1)

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