Chapter 8: Q 8.92 (page 950)

Subtract: $\frac{3}{z + 3} - \frac{6 z}{z^{2} - 9}$ .

Short Answer

Expert verified

The simplification of the rational expression is $\frac{- 3}{(z - 3)}$

Step by step solution

Given information

The given rational expression is $\frac{3}{z + 3} - \frac{6 z}{z^{2} - 9}$ .

The simplification of the rational expression

$\frac{3}{z + 3} - \frac{6 z}{z^{2} - 9}$

Factor the denominator

$= \frac{3}{z + 3} - \frac{6 z}{(z + 3) (z - 3)}$

The LCD is $(z + 3) (z - 3)$ .

localid="1648454254136" $= \frac{3 (z - 3)}{(z + 3) (z - 3)} - \frac{6 z}{(z + 3) (z - 3)} = \frac{3 z - 9}{(z + 3) (z - 3)} - \frac{6 z}{(z + 3) (z - 3)} = \frac{3 z - 9 - 6 z}{(z + 3) (z - 3)} = \frac{- 3 z - 9}{(z + 3) (z - 3)} = \frac{- 3 (z + 3)}{(z - 3) (z + 3)} = (\frac{- 3}{z - 3})$

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Subtract: $\frac{3}{z + 3} - \frac{6 z}{z^{2} - 9}$ .

Short Answer

Step by step solution

Given information

The simplification of the rational expression

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Subtract:3z+3-6zz2-9.

Short Answer

Step by step solution

Given information

The simplification of the rational expression

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Theoretical and Mathematical Physics

Applied Mathematics

Probability and Statistics

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Study anywhere. Anytime. Across all devices.

Subtract: $\frac{3}{z + 3} - \frac{6 z}{z^{2} - 9}$ .