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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q. 89 (page 667)

In the following exercises, subtract.
$\frac{5 r^{2} + 7 r - 33}{r^{2} - 49} - \frac{4 r^{2} + 5 r + 30}{r^{2} - 49}$

Short Answer

Expert verified

The resultant expression is $\frac{r + 9}{r + 7}$ .

Step by step solution

01

Step 1. Given Information

The given expression is $\frac{5 r^{2} + 7 r - 33}{r^{2} - 49} - \frac{4 r^{2} + 5 r + 30}{r^{2} - 49}$ .

02

Step 2. Subtract the numerator

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

$\begin{array}{rcl} \frac{5 r^{2} + 7 r - 33}{r^{2} - 49} - \frac{4 r^{2} + 5 r + 30}{r^{2} - 49} & = & \frac{5 r^{2} + 7 r - 33 - 4 r^{2} - 5 r - 30}{r^{2} - 49} \\ = & \frac{r^{2} + 2 r - 63}{r^{2} - 49} \end{array}$

03

Step 3. Factor the expression

Factor the expression in the numerator and denominator, and then cancel out the common terms from the numerator and denominator.

$\frac{(r - 7) (r + 9)}{(r - 7) (r + 7)} = \frac{r + 9}{r + 7}$

So, the resultant expression is $\frac{r + 9}{r + 7}$ .

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Most popular questions from this chapter

For the following exercises, perform the indicated operations.

$\frac{4 n^{2} + 32 n}{3 n + 2} . \frac{3 n^{2} - n - 2}{n^{2} + n - 30} 梅 \frac{108 n^{2} - 24 n}{n + 6}$

Simplify the rational expression $\frac{12 p - 240}{5 p - 100} .$

In the following exercises, solve each rational inequality and write the solution in interval notation.

$\frac{1}{2} + \frac{12}{x^{2}} > \frac{5}{x}$

Simplify the complex rational expression by using the LCD:

$\frac{\frac{1}{x^{2}} - \frac{1}{y^{2}}}{\frac{1}{x} + \frac{1}{y}}$

Solve each rational function inequality and write the solution in interval notation.

Given the function $R (x) = \frac{(x + 1)}{(x + 3)}$ , find the values of x that make the function less than or equal to 0.

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