Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.4 - Rational Expressions - 1.4 Exercises - Page 43: 48



Work Step by Step

$\frac{2}{a^{2}}-\frac{3}{ab}+\frac{4}{b^{2}}$ Find the lowest common denominator (i.e. $a^{2}b^{2}$) and adjust the fractions accordingly: $=\frac{2\times b^{2}}{a^{2}\times b^{2}}-\frac{3\times ab}{ab\times ab}+\frac{4\times a^{2}}{b^{2}\times a^{2}}$ Expand any brackets and simplify if possible: $=\frac{2b^{2}}{a^{2}b^{2}}-\frac{3ab}{a^{2}b^{2}}+\frac{4a^{2}}{a^{2}b^{2}}$ Combine the fractions: $=\frac{2b^{2}-3ab+4a^{2}}{a^{2}b^{2}}$
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