Precalculus (6th Edition)

Published by Pearson

Chapter 1 - Equations and Inequalities - 1.1 Linear Equations - 1.1 Exercises - Page 93: 53

Answer

$x=-\dfrac{3(a-1)}{a^{2}-a-1}$

Work Step by Step

$\dfrac{x}{a-1}=ax+3$ Take $a-1$ to multiply the right side: $x=(ax+3)(a-1)$ Evaluate the product indicated on the right side: $x=a^{2}x-ax+3a-3$ Take all terms with $x$ to the left side: $x-a^{2}x+ax=3a-3$ Take out common factor $x$ from the left side: $x(1-a^{2}+a)=3a-3$ Take $1-a^{2}+a$ to divide the right side: $x=\dfrac{3a-3}{1-a^{2}+a}$ Take out common factor $3$ from the numerator to show a better looking answer: $x=-\dfrac{3(a-1)}{a^{2}-a-1}$

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