College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter P, Prerequisites - Chapter P Review - Exercises - Page 77: 91



Work Step by Step

We multiply the numerator and denominator by $2-\sqrt{x}$ and use the fact that $(a-b)(a+b)=a^2-b^2$ to simplify: $\displaystyle \frac{x}{2+\sqrt{x}}=\frac{x}{2+\sqrt{x}}*\frac{2-\sqrt{x}}{2-\sqrt{x}}=\frac{2x-x\sqrt{x}}{2^{2}-(\sqrt{x})^{2}}=\frac{x(2-\sqrt{x})}{4-x}=\frac{x(\sqrt{x}-2)}{x-4}$
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