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: 65

Answer

$\frac{x(xy-x)}{y(xy-y)}$

Work Step by Step

Looking at the denominator of the fraction: Convert the element $y$ into a fraction $y=\frac{y}{1}$ and find the LCD: $\frac{y}{1}-\frac{y}{x}$ The LCD is $x$. Adjust the fractions accordingly: $\frac{yx}{x}-\frac{y}{x}$ Combine the fractions since they have the same denominator: $\frac{yx-y}{x}$ Looking at the numerator of the original fraction: Convert $x$ into a fraction: $\frac{x}{1}-\frac{x}{y}$ Find the LCD of the two fractions and adjust them accordingly: $\frac{xy}{y}-\frac{x}{y}$ Combine the two fractions: $\frac{xy-x}{y}$ Thus the original fraction becomes: $\frac{\frac{xy-x}{y}}{\frac{yx-y}{x}}$ Divide the fractions: $=\frac{xy-x}{y}\times\frac{x}{yx-y}$ $=\frac{x(xy-x)}{y(xy-y)}$
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