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: 81

Answer

$\displaystyle\frac{3x^{2}-7x+8}{x(x-2)^{2}}$

Work Step by Step

We create a common denominator: $\displaystyle \frac{2}{x}+\frac{1}{x-2}+\frac{3}{(x-2)^{2}}=\frac{2(x-2)^{2}}{x(x-2)^{2}}+\frac{x(x-2)}{x(x-2)^{2}}+\frac{3x}{x(x-2)^{2}}$ Then we add the top terms: $\displaystyle=\frac{2(x-2)^2+x(x-2)+3x}{x(x-2)^2}$ We distribute and simplify the top terms: =$\displaystyle \frac{2(x^{2}-4x+4)+x^{2}-2x+3x}{x(x-2)^{2}}=\frac{2x^{2}-8x+8+x^{2}-2x+3x}{x(x-2)^{2}}=\frac{3x^{2}-7x+8}{x(x-2)^{2}}$
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