Q. 224 In the following exercises, solv... [FREE SOLUTION]

91影视

Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q. 224 (page 694)

In the following exercises, solve each rational equation.
$\frac{r}{3 r - 15} - \frac{1}{4 r + 20} = \frac{3 r^{2} + 17 r + 40}{12 r^{2} - 300}$

Short Answer

Expert verified

There is no solution.

Step by step solution

Step 1. Given

The given equation is: $\frac{r}{3 r - 15} - \frac{1}{4 r + 20} = \frac{3 r^{2} + 17 r + 40}{12 r^{2} - 300}$

Step 2. To find

We have to solve the equation.

Step 3. Calculation

Factor the denominators.

$\frac{r}{3 r - 15} - \frac{1}{4 r + 20} = \frac{3 r^{2} + 17 r + 40}{12 r^{2} - 300} \frac{r}{3 (r - 5)} - \frac{1}{4 (r + 5)} = \frac{3 r^{2} + 17 r + 40}{12 (r^{2} - 25)} \frac{r}{3 (r - 5)} - \frac{1}{4 (r + 5)} = \frac{3 r^{2} + 17 r + 40}{12 (r + 5) (r - 5)}$

The denominators can never be 0. So, $r 鈮� - 5, 5$ .

We multiply both sides by the LCD and then solve the equation.

$\frac{r}{3 (r - 5)} - \frac{1}{4 (r + 5)} = \frac{3 r^{2} + 17 r + 40}{12 (r + 5) (r - 5)} \frac{r}{3 (r - 5)} 12 (r + 5) (r - 5) - \frac{1}{4 (r + 5)} 12 (r + 5) (r - 5) = \frac{3 r^{2} + 17 r + 40}{12 (r + 5) (r - 5)} 12 (r + 5) (r - 5) 4 r (r + 5) - 3 (r - 5) = 3 r^{2} + 17 r + 40 4 r^{2} + 20 r - 3 r + 15 = 3 r^{2} + 17 r + 40 4 r^{2} + 17 r + 15 = 3 r^{2} + 17 r + 40 r^{2} - 25 = 0 (r + 5) (r - 5) = 0 r = - 5, 5$

But $r 鈮� - 5, 5$ . So there is no solution.

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91影视

In the following exercises, solve each rational equation.
$\frac{r}{3 r - 15} - \frac{1}{4 r + 20} = \frac{3 r^{2} + 17 r + 40}{12 r^{2} - 300}$

Short Answer

Step by step solution

Step 1. Given

Step 2. To find

Step 3. Calculation

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91影视

In the following exercises, solve each rational equation. r3r-15-14r+20=3r2+17r+4012r2-300

Short Answer

Step by step solution

Step 1. Given

Step 2. To find

Step 3. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Probability and Statistics

Calculus

Mechanics Maths

Decision Maths

Pure Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, solve each rational equation.
$\frac{r}{3 r - 15} - \frac{1}{4 r + 20} = \frac{3 r^{2} + 17 r + 40}{12 r^{2} - 300}$