# Chapter 1 - Section 1.4 - Rational Expressions - 1.4 Exercises: 40

$\frac{x-4}{x+1}$

#### Work Step by Step

$\frac{3x-2}{x+1}-2$ Convert the element 2 to a fraction: $=\frac{3x-2}{x+1}-\frac{2}{1}$ Multiply the element by the denominator of the fraction containing variables: $=\frac{3x-2}{x+1}-\frac{2\times (x+1)}{1\times (x+1)}$ Expand the fraction: $=\frac{3x-2}{x+1}-\frac{2x+2}{x+1}$ Combine the fractions: $=\frac{3x-2-(2x+2)}{x+1}$ Expand the negative sign: $=\frac{3x-2-2x-2}{x+1}$ Collect the like terms: $=\frac{x-4}{x+1}$

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