Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 7 - Review: 42


$x=-4$ and $x=3$

Work Step by Step

$\dfrac{2}{x+1}-\dfrac{1}{x-2}=-\dfrac{1}{2}$ Multiply the whole equation by $2(x+1)(x-2)$: $2(x+1)(x-2)\Big(\dfrac{2}{x+1}-\dfrac{1}{x-2}=-\dfrac{1}{2}\Big)$ $2(2)(x-2)-2(x+1)=-(x+1)(x-2)$ Evaluate all the products: $4x-8-2x-2=-x^{2}+x+2$ Take all terms to the left side of the equation: $x^{2}-x-2+4x-8-2x-2=0$ Simplify the equation by combining like terms: $x^{2}+x-12=0$ Solve this equation by factoring: $(x+4)(x-3)=0$ Set each factor equal to $0$ and solve each individual equation: $x+4=0$ $x=-4$ $x-3=0$ $x=3$ The initial equation is not undefined for neither of these two values of $x$, so the solutions are: $x=-4$ and $x=3$
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