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

Step 1. Given Information

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

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.

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

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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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

Step by step solution

Step 1. Given Information

Step 2. Subtract the numerator

Step 3. Factor the expression

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In the following exercises, subtract.5r2+7r-33r2-49-4r2+5r+30r2-49

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Subtract the numerator

Step 3. Factor the expression

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Decision Maths

Calculus

Logic and Functions

Geometry

Statistics

Study anywhere. Anytime. Across all devices.

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