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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q. 7.38 (page 662)

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

Short Answer

Expert verified

The difference of the given rational expressions is $\frac{- 3}{z - 3}$ .

Step by step solution

01

Step 1. Given information

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

02

Step 2. Find the LCD

Factor the denominator of the second rational expressions.

$z^{2} - 9 = (z - 3) (z + 3)$

So, the LCD is

03

Step 3. Express the expression with LCD

Express the expression with LCD .

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

04

Step 4. Subtract the obtained Expressions

Subtract the obtained equivalent expressions and simplify by canceling out the common terms in numerator and denominator.

$\begin{array}{rcl} \frac{3 z - 9}{(z - 3) (z + 3)} - \frac{6 z}{(z - 3) (z + 3)} & = & \frac{3 z - 9 - 6 z}{(z - 3) (z + 3)} \\ = & \frac{- 9 - 3 z}{(z - 3) (z + 3)} \\ = & \frac{- 3 (z + 3)}{(z - 3) (z + 3)} \\ = & \frac{- 3}{z - 3} \end{array}$

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Most popular questions from this chapter

If $a$ varies directly as $b$ and $a = 16$ , when $b = 4$ . Find the equation that relates $a$ and $b$ .

Determine the values for which the rational expression is undefined.

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Divide $\frac{11 + w}{w - 9} 梅 \frac{121 - w^{2}}{9 - w}$

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$R (x) = \frac{x^{3} - 2 x^{2} - 25 x + 50}{x^{2} - 25}$

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