Chapter 8: Q. 341 (page 982)

In the following exercises, solve
$\frac{s}{2 s + 6} - \frac{2}{5 s + 5} = \frac{5 s^{2} - s - 18}{10 s^{2} + 40 s + 30}$

Short Answer

Expert verified

The answer is $s = - 3 .$

Step by step solution

Step 1. Given Information

The given rational equation is $\frac{s}{2 s + 6} - \frac{2}{5 s + 5} = \frac{5 s^{2} - s - 18}{10 s^{2} + 40 s + 30}$

Step 2. Least Common Denominator(LCD)

On Simplifying the given equation,

$\frac{s}{2 s + 6} - \frac{2}{5 s + 5} = \frac{5 s^{2} - s - 18}{10 s^{2} + 40 s + 30} \frac{s}{2 (s + 3)} - \frac{2}{5 (s + 1)} = \frac{5 s^{2} - s - 18}{10 (s^{2} + 4 s + 3)} \frac{s}{2 (s + 3)} - \frac{2}{5 (s + 1)} = \frac{5 s^{2} - s - 18}{10 (s^{2} + 3 s + s + 3)} \frac{s}{2 (s + 3)} - \frac{2}{5 (s + 1)} = \frac{5 s^{2} - s - 18}{10 (s + 1) (s + 3)}$

Therefore, LCD is $10 (s + 1) (s + 3)$

Step 3. Clearing fractions

Multiply all terms by LCD,

$10 (s + 1) (s + 3) [\frac{s}{2 (s + 3)} - \frac{2}{5 (s + 1)}] = \frac{5 s^{2} - s - 18}{10 (s + 1) (s + 3)} \times 10 (s + 1) (s + 3) 5 (s + 1) (s) - 4 (s + 3) = 5 s^{2} - s - 18 5 s^{2} + 5 s - 4 s - 12 = 5 s^{2} - s - 18 2 s + 6 = 0 s = - \frac{6}{2} s = - 3$

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In the following exercises, solve
$\frac{s}{2 s + 6} - \frac{2}{5 s + 5} = \frac{5 s^{2} - s - 18}{10 s^{2} + 40 s + 30}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Least Common Denominator(LCD)

Step 3. Clearing fractions

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In the following exercises, solves2s+6-25s+5=5s2-s-1810s2+40s+30

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Least Common Denominator(LCD)

Step 3. Clearing fractions

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Geometry

Calculus

Decision Maths

Pure Maths

Statistics

Study anywhere. Anytime. Across all devices.

In the following exercises, solve
$\frac{s}{2 s + 6} - \frac{2}{5 s + 5} = \frac{5 s^{2} - s - 18}{10 s^{2} + 40 s + 30}$