Chapter 8: Q 8.90 (page 948)

Subtract: $\frac{z + 3}{z + 2} - \frac{z}{z + 3}$

Short Answer

Expert verified

The simplification of the expression is $\frac{3}{z + 3}$ .

Step by step solution

Given information

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

The simplification of the expression

$\frac{z + 3}{z + 2} - \frac{z}{z + 3}$

The LCD of the rational expression is $(z + 2) (z + 3)$ .

Change into equivalent fractions with the LCD $(z + 2) (z + 3)$ .

role="math" localid="1648455874752" $= \frac{(z + 3) (z + 2)}{(z + 2) (z + 3)} - \frac{z (z + 2)}{(z + 3) (z + 2)} = \frac{z^{2} + 3 z + 2 z + 6}{(z + 2) (z + 3)} - \frac{z^{2} + 2 z}{(z + 2) (z + 3)} S i m p l i f y = \frac{z^{2} + 5 z + 6 - z^{2} - 2 z}{(z + 2) (z + 3)} = \frac{3 z + 6}{(z + 2) (z + 3)} = \frac{3 (z + 2)}{(z + 2) (z + 3)} = \frac{3}{(z + 3)}$

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Subtract: $\frac{z + 3}{z + 2} - \frac{z}{z + 3}$

Short Answer

Step by step solution

Given information

The simplification of the expression

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Subtract:z+3z+2-zz+3

Short Answer

Step by step solution

Given information

The simplification of the expression

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Theoretical and Mathematical Physics

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Applied Mathematics

Study anywhere. Anytime. Across all devices.

Subtract: $\frac{z + 3}{z + 2} - \frac{z}{z + 3}$