Chapter 8: Q 8.93 (page 950)

Subtract: $\frac{3 x - 1}{x^{2} - 5 x - 6} - \frac{2}{6 - x}$

Short Answer

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The simplification of the expression is $\frac{5 x + 1}{(x + 1) (x - 6)}$ .

Step by step solution

Given information

The given rational expression is $\frac{3 x - 1}{x^{2} - 5 x - 6} - \frac{2}{6 - x}$ .

The simplification of the rational expression

$= \frac{3 x - 1}{x^{2} - 5 x - 6} - \frac{2}{6 - x}$

Factor the denominator

$= \frac{3 x - 1}{x^{2} - 6 x + x - 6} - \frac{2}{6 - x} = \frac{3 x - 1}{x (x - 6) + (x - 6)} - \frac{2}{6 - x} = \frac{3 x - 1}{(x + 1) (x - 6)} - \frac{2}{6 - x}$

Since $(n - 6) a n d (6 - n)$ are opposites ,we will multiply the second rational expression by $\frac{- 1}{- 1}$ .

$= \frac{3 x - 1}{(x + 1) (x - 6)} - \frac{(- 2)}{- (6 - x)} = \frac{3 x - 1}{(x + 1) (x - 6)} - \frac{- 2}{(x - 6)}$

The LCD of the rational expression is $(x + 1) (x - 6)$ .

Rewrite each rational expression as an equivalent rational expression with the LCD.

localid="1657069728617" $= \frac{3 x - 1}{(x + 1) (x - 6)} - \frac{- 2 (x + 1)}{(x - 6) (x + 1)} S i m p l i f y = \frac{3 x - 1 + 2 x + 2}{(x + 1) (x - 6)} = \frac{5 x + 1}{(x + 1) (x - 6)}$

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Subtract: $\frac{3 x - 1}{x^{2} - 5 x - 6} - \frac{2}{6 - x}$

Short Answer

Step by step solution

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The simplification of the rational expression

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Subtract:3x-1x2-5x-6-26-x

Short Answer

Step by step solution

Given information

The simplification of the rational expression

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Most popular questions from this chapter

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Subtract: $\frac{3 x - 1}{x^{2} - 5 x - 6} - \frac{2}{6 - x}$