## Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole

# Chapter 1 - Section 1.4 - Rational Expressions - 1.4 Exercises: 55

#### Answer

$\frac{5x-6}{x(x-1)}$

#### Work Step by Step

$\frac{2}{x}+\frac{3}{x-1}-\frac{4}{x^{2}-x}$ Factor the expression $x^{2}-x$ and replace in denominator: $=\frac{2}{x}+\frac{3}{x-1}-\frac{4}{x(x-1)}$ Find the lowest common denominator (i.e. $x(x-1)$) and adjust the fractions accordingly: $=\frac{2\times (x-1)}{x\times (x-1)}+\frac{3\times x}{(x-1) \times x}-\frac{4}{x(x-1)}$ $=\frac{2(x-1)}{x(x-1)}+\frac{3x}{x(x-1)}-\frac{4}{x(x-1)}$ Combine the fractions: $=\frac{2(x-1)+3x-4}{x(x-1)}$ Expand any brackets in the numerator: $=\frac{2x-2+3x-4}{x(x-1)}$ Simplify: $=\frac{5x-6}{x(x-1)}$

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