Algebra: A Combined Approach (4th Edition)

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

Chapter 7 - Review: 44

Answer

$x=5$

Work Step by Step

$\dfrac{2}{x-3}-\dfrac{4}{x+3}=\dfrac{8}{x^{2}-9}$ Factor the denominator of the fraction on the right side of the equation: $\dfrac{2}{x-3}-\dfrac{4}{x+3}=\dfrac{8}{(x-3)(x+3)}$ Multiply the whole equation by $(x-3)(x+3)$ $(x-3)(x+3)\Big[\dfrac{2}{x-3}-\dfrac{4}{x+3}=\dfrac{8}{(x-3)(x+3)}\Big]$ $2(x+3)-4(x-3)=8$ $2x+6-4x+12=8$ Take the $8$ to the left side of the equation and simplify the equation by combining like terms: $2x+6-4x+12-8=0$ $-2x+10=0$ Solve for $x$: $-2x=-10$ $x=\dfrac{-10}{-2}$ $x=5$ The initial equation is not undefine for the value of $x$ found. So the solution to this equation is $x=5$
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