Algebra: A Combined Approach (4th Edition)

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

Chapter 7 - Section 7.5 - Solving Equations Containing Rational Expressions - Exercise Set: 31

Answer

$x=0$

Work Step by Step

$\dfrac{2}{x-2}+1=\dfrac{x}{x+2}$ Multiply the whole equation by $(x-2)(x+2)$ to eliminate all denominators: $(x-2)(x+2)\Big(\dfrac{2}{x-2}+1=\dfrac{x}{x+2}\Big)$ $2(x+2)+(x-2)(x+2)=x(x-2)$ Evaluate the indicated operations: $2x+4+x^{2}-4=x^{2}-2x$ Take all terms to the left side of the equation and simplify it by combining like terms: $x^{2}-x^{2}+2x+2x+4-4=0$ $4x=0$ Solve for $x$: $x=0$
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