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: 67



Work Step by Step

Looking at the denominator: Find the LCD (i.e. $x^{2}y^{2}$) and adjust accordingly: $=\frac{y^{2}}{x^{2}y^{2}}-\frac{x^{2}}{x^{2}y^{2}}$ $=\frac{y^{2}-x^{2}}{x^{2}y^{2}}$ Looking at the numerator: Find the LCD (i.e. $xy$) and adjust accordingly: $=\frac{x^{2}}{xy}-\frac{y^{2}}{xy}$ $=\frac{x^{2}-y^{2}}{xy}$ This then becomes: $=\frac{\frac{x^{2}-y^{2}}{xy}}{\frac{y^{2}-x^{2}}{x^{2}y^{2}}}$ Divide the fractions: $=\frac{x^{2}-y^{2}}{xy}\times\frac{x^{2}y^{2}}{y^{2}-x^{2}}$ $=\frac{(x^{2}-y^{2})\times x^{2}y^{2}}{xy\times(y^{2}-x^{2})}$ $=-\frac{(x^{2}-y^{2})\times x^{2}y^{2}}{xy\times(x^{2}-y^{2})}$ Cancel out the common factors: $=-\frac{x^{2}y^{2}}{xy}$ $=-xy$
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