Chapter 7 - Section 7.5 - Solving Equations Containing Rational Expressions - Exercise Set - Page 524: 33

x = -2

$\frac{x+1}{3}$-$\frac{x-1}{6}$=$\frac{1}{6}$ 6($\frac{x+1}{3}$-$\frac{x-1}{6}$)=6$\frac{1}{6}$ 6$\frac{x+1}{3}$-6$\frac{x-1}{6}$=6$\frac{1}{6}$ 2(x+1)-(x-1)=1 2x+2-x+1=1 x+3=1 x=1-3 x=-2 The solution is -2 Check Let x=-2 $\frac{-2+1}{3}$-$\frac{-2-1}{6}$=$\frac{1}{6}$ -$\frac{1}{3}$-$\frac{-3}{6}$=$\frac{1}{6}$ -$\frac{2}{6}$+$\frac{3}{6}$=$\frac{1}{6}$ $\frac{1}{3}$=$\frac{1}{6}$