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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

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

01

Given information

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

02

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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