Chapter 11: Q. 178 (page 1069)

Simplify a Complex Rational Expression by Using the LCD.
In the following exercises, simplify each complex rational expression by using the LCD. $\frac{\frac{3}{s + 6} + \frac{5}{s - 6}}{\frac{1}{s^{2} - 36} + \frac{4}{s + 6}}$

Short Answer

Expert verified

The simplification is $\frac{8 s + 12}{4 s - 23}$ .

Step by step solution

Step 1. Given.

The given complex rational expression is: $\frac{\frac{3}{s + 6} + \frac{5}{s - 6}}{\frac{1}{s^{2} - 36} + \frac{4}{s + 6}}$ .

Step 2. To find

We have to simplify each complex rational expression by using the LCD.

Step 3. Calculation

LCM of the denominators is = $(s + 6) (s - 6)$ . Multiply numerator and denominator by it to simplify.

$\frac{\frac{3}{s + 6} + \frac{5}{s - 6}}{\frac{1}{s^{2} - 36} + \frac{4}{s + 6}} = \frac{\frac{3}{s + 6} (s + 6) (s - 6) + \frac{5}{s - 6} (s + 6) (s - 6)}{\frac{1}{s^{2} - 36} (s + 6) (s - 6) + \frac{4}{s + 6} (s + 6) (s - 6)} = \frac{3 (s - 6) + 5 (s + 6)}{1 + 4 (s - 6)} = \frac{3 s - 18 + 5 s + 30}{1 + 4 s - 24} = \frac{8 s + 12}{4 s - 23}$

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Simplify a Complex Rational Expression by Using the LCD.
In the following exercises, simplify each complex rational expression by using the LCD. $\frac{\frac{3}{s + 6} + \frac{5}{s - 6}}{\frac{1}{s^{2} - 36} + \frac{4}{s + 6}}$

Short Answer

Step by step solution

Step 1. Given.

Step 2. To find

Step 3. Calculation

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Simplify a Complex Rational Expression by Using the LCD.In the following exercises, simplify each complex rational expression by using the LCD.3s+6+5s-61s2-36+4s+6

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

Applied Mathematics

Calculus

Logic and Functions

Mechanics Maths

Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Simplify a Complex Rational Expression by Using the LCD.
In the following exercises, simplify each complex rational expression by using the LCD. $\frac{\frac{3}{s + 6} + \frac{5}{s - 6}}{\frac{1}{s^{2} - 36} + \frac{4}{s + 6}}$