Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 6 - Rational Expressions and Equations - 6.6 Rational Equations - 6.6 Exercise Set - Page 416: 30


No solution

Work Step by Step

In order to solve rational equations, we try to get the variable by itself on one side of the equation. It is important to remember that there are many ways to do this. For instance, we could combine the different fractions and then simplify, or we could multiply both sides of the equation by the least common denominator. In addition, we may need previously learned methods of solving equations, such as factoring. Thus, solving the rational equation, we obtain: $$ \frac{3}{a+7}\left(a+7\right)=\frac{a+10}{a+7}\left(a+7\right)\\ a+10=3\\ a=-7$$ Since this makes the denominator zero, there is no solution.
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