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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset Vaia Explanations$ Math

2nd Edition · 1240 pages

ISBN: 9780998625713

Chapter 8: Q 8.95 (page 951)

Subtract: $\frac{2 x + 7}{x - 7} - 3$

Short Answer

Expert verified

The subtract of rational expressions is $\frac{- x + 22}{x - 7}$

Step by step solution

01

Given information

The given rational expressions is $\frac{2 x - 7}{x - 7} - 3$

02

The simplification of the rational expressions

Write 3 as $\frac{3}{1}$ to have 2 rational expressions.

The LCD of $x - 7 and 1 is (x - 7)$ .

Rewrite $\frac{3}{1}$ as an equivalent expression with the LCD.

$\frac{2 x + 1}{x - 7} - \frac{3 (x - 7)}{1 (x - 7)} Simplify \frac{2 x + 1}{x - 7} - \frac{3 x - 21}{x - 7} \frac{2 x + 1 - 3 x + 21}{x - 7} Simplify \frac{- x + 22}{x - 7}$

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Most popular questions from this chapter

In the following exercises, simplify.

$\frac{12 p - 240}{5 p - 100}$

Electronics The resistance of a circuit formed by connecting two resistors in parallel is $\frac{1}{\frac{1}{R_{1}} + \frac{1}{R_{2}}}$ .

Simplify the complex fraction role="math" localid="1647789125778" $\frac{1}{\frac{1}{R_{1}} + \frac{1}{R_{2}}}$ .
Find the resistance of the circuit when $R_{1} = 8$ and $R_{2} = 12$ .

Solve :

$1 - \frac{2}{a} = \frac{15}{a^{2}}$

In the following exercises, solve.

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