Chapter 8: Q. 324 (page 982)

In the following exercises, solve.
$\frac{3}{r + 10} - \frac{4}{r - 4} = 1$

Short Answer

Expert verified

The answer is $r = - 3, - 4 .$

Step by step solution

Step 1. Given Information

A radical expression is given as

$\frac{3}{r + 10} - \frac{4}{r - 4} = 1$

Step 2. Clearing the fractions

The least common denominator is $(r - 4) (r + 10)$

Multiply the equation by LCD,

localid="1647779805341" $(r + 10) (r - 4) \{\frac{3}{r + 10} - \frac{4}{r - 4}\} = 1 (r + 10) (r - 4) (r - 4) (3) - {4 (r + 10)} = r^{2} - 4 r + 10 r - 40 3 r - 12 - {4 r + 40) = r^{2} + 6 r - 40 3 r - 12 - 4 r - 40 = r^{2} + 6 r - 40 r^{2} + 7 r + 12 = 0$

Step 3. Solution of the equation

Now, solving the quadratic equation,

$r^{2} + 7 r + 12 = 0 r^{2} + 3 r + 4 r + 12 = 0 r (r + 3) + 4 (r + 3) = 0 (r + 4) (r + 3) = 0$

Using the Zero product property,

$r + 4 = 0 r = - 4 r + 3 = 0 r = - 3$

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In the following exercises, solve.
$\frac{3}{r + 10} - \frac{4}{r - 4} = 1$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Clearing the fractions

Step 3. Solution of the equation

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In the following exercises, solve.3r+10-4r-4=1

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Clearing the fractions

Step 3. Solution of the equation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Mechanics Maths

Pure Maths

Geometry

Probability and Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In the following exercises, solve.
$\frac{3}{r + 10} - \frac{4}{r - 4} = 1$