Chapter 8: Q. 281 (page 966)

In the following exercises, simplify.
$\frac{\frac{5}{z^{2} - 64} + \frac{3}{z + 8}}{\frac{1}{z + 8} + \frac{2}{z - 8}}$

Short Answer

Expert verified

The Simplified Expression is $\frac{3 z - 19}{3 z + 8}$

Step by step solution

Step 1. Given Information

The given Expression is

$\frac{\frac{5}{z^{2} - 64} + \frac{3}{z + 8}}{\frac{1}{z + 8} + \frac{2}{z - 8}}$

Step 2. Simplify the Expression

$\frac{\frac{5}{z^{2} - 64} + \frac{3}{z + 8}}{\frac{1}{z + 8} + \frac{2}{z - 8}} = \frac{(z + 8) (z - 8) (\frac{5}{(z + 8) (z - 8)}) + (z + 8) (z - 8) (\frac{3}{(z + 8)})}{(z + 8) (z - 8) (\frac{1}{(z + 8)} + \frac{2}{(z - 8)})} = \frac{5 + 3 (z - 8)}{z - 8 + 2 (z + 8)} = \frac{5 + 3 z - 24}{z - 8 + 2 z + 16} = \frac{- 19 + 3 z}{3 z + 8} = \frac{3 z - 19}{3 z + 8}$

The simplified expression is $\frac{3 z - 19}{3 z + 8}$

Step 3. The solution

The simplified expression is $\frac{3 z - 19}{3 z + 8}$

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In the following exercises, simplify.
$\frac{\frac{5}{z^{2} - 64} + \frac{3}{z + 8}}{\frac{1}{z + 8} + \frac{2}{z - 8}}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Simplify the Expression

Step 3. The solution

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In the following exercises, simplify.5z2-64+3z+81z+8+2z-8

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Simplify the Expression

Step 3. The solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

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Calculus

Study anywhere. Anytime. Across all devices.

In the following exercises, simplify.
$\frac{\frac{5}{z^{2} - 64} + \frac{3}{z + 8}}{\frac{1}{z + 8} + \frac{2}{z - 8}}$