Chapter 8: Q 8.96 (page 951)

Subtract $\frac{4 y + 3}{2 y - 1} - 5$

Short Answer

Expert verified

The simplification of the rational expression is $\frac{- 6 y + 8}{2 y - 1}$ .

Step by step solution

Given information

The given rational expression is $\frac{4 y + 3}{2 y - 1} - 5$

The simplification of the rational expression

Write 5 as $\frac{5}{1}$ to have 5 rational expressions .

The LCD of $2 y - 1 and 1 is (2 y - 1)$ .

Rewrite $\frac{5}{1}$ as an equivalent rational expressions with the LCD.

$\frac{4 y + 3}{2 y - 1} - \frac{5 (2 y - 1)}{1 (2 y - 1)}$

Simplify

$= \frac{4 y + 3}{2 y - 1} - \frac{5 (2 y - 1)}{1 (2 y - 1)} S i m p l i f y = \frac{4 y + 3}{2 y - 1} - \frac{10 y - 5}{2 y - 1} = \frac{4 y + 3 - 10 y + 5}{2 y - 1} = \frac{- 6 y + 8}{2 y - 1} Factor common factors \frac{- 6 y + 8}{2 y - 1}$

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Subtract $\frac{4 y + 3}{2 y - 1} - 5$

Short Answer

Step by step solution

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The simplification of the rational expression

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Short Answer

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Subtract $\frac{4 y + 3}{2 y - 1} - 5$