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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 434 (page 737)

In the following exercise, simplify
$\frac{\frac{3}{y^{2} - 4 y - 32}}{\frac{2}{y - 8} - \frac{1}{y + 4}}$

Short Answer

Expert verified

The solution is $\frac{3}{y + 16}$

Step by step solution

01

Step 1, Given information

$\frac{\frac{3}{y^{2} - 4 y - 32}}{\frac{2}{y - 8} - \frac{1}{y + 4}}$

02

Step 2. Simplify

The LCD of all fractions in the complex rational expression is $(y - 8) (y + 4)$

Multiply the numerator and denominator by the LCD.

$\frac{(y - 8) (y + 4) (\frac{3}{y^{2} - 4 y - 32})}{(y - 8) (y + 4) (\frac{2}{y - 8} - \frac{1}{y + 4})} = \frac{(y - 8) (y + 4) (\frac{3}{y^{2} - 4 y - 32})}{((y - 8) (y + 4) \frac{2}{y - 8} - (y - 8) (y + 4) \frac{1}{y + 4})} = \frac{\frac{3}{1}}{\frac{2 (y + 4) - (y - 8)}{1}}$

Rewrite as fraction division.

$= \frac{3}{1} 梅 \frac{2 (y + 4) - (y - 8)}{1}$

Multiply the first times the reciprocal of the second, and simplify.

$= \frac{3}{2 (y + 4) - (y - 8)} = \frac{3}{y + 16}$

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Most popular questions from this chapter

In the following exercises, perform the indicated operations

$\frac{5 q}{p^{2} q - p^{2}} + \frac{4 q}{q^{2} - 1}$

Joon drove 4 hours to his home, driving 208 miles on the interstate and 40 miles on the country roads. If he drove 15 mph faster on the interstate than on the country roads, what was his rate on the country roads?

Divide the rational expression $\frac{3 y^{2} - 12 y - 63}{4 y + 3} 梅 (6 y^{2} - 42 y)$

For the following exercises, find $R (x) = f (x) g (x)$ where $f (x) a n d g (x)$ are given.

$f (x) = \frac{x^{2} - 2 x}{x^{2} + 6 x - 16} a n d g (x) = \frac{x^{2} - 64}{x^{2} - 8 x}$

For the following exercises, find $R (x) = f (x) . g (x)$ where $f (x) a n d g (x)$ are given.

localid="1644679377284" $f (x) = \frac{6 x^{2} - 12 x}{x^{2} + 7 x - 18} a n d g (x) = \frac{x^{2} - 81}{3 x^{2} - 27 x}$

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