Chapter 8: Q. 326 (page 982)

In the following exercises, solve.
$\frac{2}{s + 7} - \frac{3}{s - 3} = 1$

Short Answer

Expert verified

The answer is $s = - 2, - 3 .$

Step by step solution

Step 1. Given information

The given rational expression is

$\frac{2}{s + 7} - \frac{3}{s - 3} = 1$

Step 2. Eliminating the fractions

The Least Common denominator is $(s + 7) (s - 3)$

Multiply the equation by LCD

$(s + 7) (s - 3) {\frac{2}{s + 7} - \frac{3}{s - 3}} = 1 (s + 7) (s - 3) 2 (s - 3) - 3 (s + 7) = s^{2} - 3 s + 7 s - 21 2 s - 6 - 3 s - 21 = s^{2} + 4 s - 21 - s - 27 = s^{2} + 4 s - 21 s^{2} + 5 s + 6 = 0$

Step 3. Solving the Quadratic equation

The equation can be written as:

$s^{2} + 5 s + 6 = 0$

$s^{2} + 2 s + 3 s + 6 = 0 s (s + 2) + 3 (s + 2) = 0 (s + 3) (s + 2) = 0$

Using the Zero product property,

$s + 3 = 0; s + 2 = 0 s = - 3, s = - 2$

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In the following exercises, solve.
$\frac{2}{s + 7} - \frac{3}{s - 3} = 1$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Eliminating the fractions

Step 3. Solving the Quadratic equation

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In the following exercises, solve.2s+7-3s-3=1

Short Answer

Step by step solution

Step 1. Given information

Step 2. Eliminating the fractions

Step 3. Solving the Quadratic equation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Applied Mathematics

Geometry

Pure Maths

Probability and Statistics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, solve.
$\frac{2}{s + 7} - \frac{3}{s - 3} = 1$