# Chapter 7 - Section 7.5 - Integrated Review - Summary on Rational Expressions - Page 526: 8

The solution is 1

#### Work Step by Step

$\frac{4}{x-3}$-$\frac{1}{x}$=$\frac{6}{x(x-3)}$ x(x-3)[$\frac{4}{x-3}$-$\frac{1}{x}$]=x(x-3)$\frac{6}{x(x-3)}$ x(x-3)$\frac{4}{x-3}$-x(x-3)$\frac{1}{x}$=x(x-3)$\frac{6}{x(x-3)}$ 4x-(x-3)=6 4x-x+3=6 3x+3=6 3x=6-3 3x=3 x=1 The solution is 1 Check Let x=1 $\frac{4}{x-3}$-$\frac{1}{x}$=$\frac{6}{x(x-3)}$ $\frac{4}{1-3}$-$\frac{1}{1}$=$\frac{6}{1(1-3)}$ $\frac{4}{-2}$-1=$\frac{6}{-2}$ -2-1=-3 -3=-3

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