Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 11 - Rational Expressions and Functions - Mid-Chapter Quiz: 22

Answer

a) Your friend's mistake is claiming that $x-3$ and $3-x$ are common factors. In fact, they are not. Imagine plugging in 4 for x. $x-3 = 4-3 = 1$. However, $3-x = 3-4 = -1$, showing that these are not equivalent expressions. b) You can factor out a negative from our second term: $\frac{x}{3-x}$, making it $-\frac{x}{x - 3}$. Now we have the common term $x-3$ that can cancel.

Work Step by Step

a) Your friend's mistake is claiming that $x-3$ and $3-x$ are common factors. In fact, they are not. Imagine plugging in 4 for x. $x-3 = 4-3 = 1$. However, $3-x = 3-4 = -1$, showing that these are not equivalent expressions. b) You can factor out a negative from our second term: $\frac{x}{3-x}$, making it $-\frac{x}{x - 3}$. Now we have the common term $x-3$ that can cancel.
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