Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0



The equation has no solution.

Work Step by Step

$\dfrac{-x}{x+1}-\dfrac{1}{x-1}=\dfrac{-2}{x^{2}-1}$ Factor the denominator of the fraction on the right side of the equation: $\dfrac{-x}{x+1}-\dfrac{1}{x-1}=\dfrac{-2}{(x-1)(x+1)}$ Multiply the whole equation by $(x-1)(x+1)$: $(x-1)(x+1)\Big[\dfrac{-x}{x+1}-\dfrac{1}{x-1}=\dfrac{-2}{(x-1)(x+1)}\Big]$ $-x(x-1)-(x+1)=-2$ Evaluate the indicated operations: $-x^{2}+x-x-1=-2$ Take $2$ to the left side and simplify: $-x^{2}+x-x-1+2=0$ $-x^{2}+1=0$ Rearrange: $x^{2}-1=0$ Solve by factoring: $(x-1)(x+1)=0$ Set both factors equal to $0$ and solve each individual equation for $x$: $x-1=0$ $x=1$ $x+1=0$ $x=-1$ The original equation is undefined for $x=1$ and $x=-1$, so it has no solution.
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