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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 7: Q. 125 (page 668)

In the following exercises, perform indicated operations.

Short Answer

Expert verified

The resultant expression is $\frac{- 6}{m + 6}$ .

Step by step solution

01

Step 1. Given Information

The given expression is $\frac{6}{m + 6} - \frac{12 m}{m^{2} - 36}$ .

02

Step 2. Express with LCD

The LCD of the given expressions to subtract is $(m - 6) (m + 6)$ .
Express the given expression with LCD.

$\frac{6}{m + 6} - \frac{12 m}{m^{2} - 36} = \frac{6 m - 36}{(m + 6) (m - 6)} - \frac{12 m}{(m + 6) (m - 6)}$

03

Step 3. Simplify

As the denominator is the same for both the terms, perform addition in the numerator and place it over the common denominator.

$\begin{array}{rcl} \frac{6 m - 36}{(m + 6) (m - 6)} - \frac{12 m}{(m + 6) (m - 6)} & = & \frac{6 m - 36 - 12 m}{(m + 6) (m - 6)} \\ = & \frac{- 6 m - 36}{(m + 6) (m - 6)} \end{array}$

Cancel out the common factor from numerator and denominator.

$\begin{array}{rcl} \frac{- 6 m - 36}{(m + 6) (m - 6)} & = & \frac{- 6 (m + 6)}{(m + 6) (m - 6)} \\ = & \frac{- 6}{m + 6} \end{array}$

So, the resultant expression is $\frac{- 6}{m + 6}$ .

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Most popular questions from this chapter

In the following exercise, find

(a) $R (x) = f (x) + g (x)$

(b) $R (x) = f (x) - g (x)$ :

$f (x) = \frac{6 x}{x^{2} - 64} g (x) = \frac{3}{x - 8}$

In the following exercises, find the domain of each function.

$R (x) = \frac{x^{3} + 3 x^{2} - 4 x - 12}{x^{2} - 4}$

In the following exercises, divide the rational expressions.

$\frac{x^{2} + 3 x - 10}{4 x} \div (2 x^{2} + 20 x + 50)$

In the following exercises, divide the rational expressions.

$\frac{\frac{2 a^{2} - a - 21}{5 a + 20}}{\frac{a^{2} + 7 a + 12}{a^{2} + 8 a + 16}}$

Write the steps to find the solution to the given equation.

See all solutions

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