Algebra: A Combined Approach (4th Edition)

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

Chapter 7 - Section 7.7 - Simplifying Complex Fractions - Exercise Set: 19

Answer

$\dfrac{\dfrac{1}{5}-\dfrac{1}{x}}{\dfrac{7}{10}+\dfrac{1}{x^{2}}}=\dfrac{2x(x-5)}{7x^{2}+10}$

Work Step by Step

$\dfrac{\dfrac{1}{5}-\dfrac{1}{x}}{\dfrac{7}{10}+\dfrac{1}{x^{2}}}$ Evaluate the substraction indicated in the numerator and the sum indicated in the denominator: $\dfrac{\dfrac{1}{5}-\dfrac{1}{x}}{\dfrac{7}{10}+\dfrac{1}{x^{2}}}=\dfrac{\dfrac{x-5}{5x}}{\dfrac{7x^{2}+10}{10x^{2}}}=...$ Evaluate the division and simplify if possible: $...=\dfrac{x-5}{5x}\div\dfrac{7x^{2}+10}{10x^{2}}=\dfrac{(x-5)(10x^{2})}{(7x^{2}+10)(5x)}=...$ $...=\dfrac{(x-5)(2x)}{7x^{2}+10}=\dfrac{2x(x-5)}{7x^{2}+10}$
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