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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 11: Q. 23 (page 1069)

Simplify the rational expression $\frac{20 - 5 y}{y^{2} - 16}$

Short Answer

Expert verified

The simplified form of $\frac{20 - 5 y}{y^{2} - 16} i s \frac{- 5}{(y + 4)}, y 鈮� - 4 .$

Step by step solution

01

. Given information

Given rational expression is $\frac{20 - 5 y}{y^{2} - 16}$ .

We have to simplify the given rational expression.

02

. Simplification of the rational expression

To simply first we need to factor both numerator and denominator separately and find out the common factor, then simplify,
$\frac{20 - 5 y}{y^{2} - 16} = \frac{5 (4 - y)}{(y + 4) (y - 4)} = \frac{- 5 (y - 4)}{(y + 4) (y - 4)}, a n e x p r e s s i o n a n d i t s o p p o s i t e t o d i v i d e s i s - 1 = \frac{- 5}{(y + 4)}; y 鈮� - 4, c o m m o n f a c t o r d i v i d e o u t . T h i s i s t h e s i m p l i f i e d f o r m o f t h e g i v e n e x p r e s s i o n .$

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Most popular questions from this chapter

In the following exercises, factor each trinomial of the form

$x^{2} + b x + c x^{2} - 12 - 11 x$

In the following exercises, factor each expression using any method $6 r^{2} + 30 r + 36$

Explain why an equation of the form $\sqrt{x} + 1 = 0$ has no solution.

Simplify

(a) ${(\frac{1}{2} y^{2})}^{3} {(\frac{2}{3} y)}^{2}$

(b) ${(\frac{1}{2} j^{2})}^{5} {(\frac{2}{5} j^{3})}^{2}$

In the following exercise, find

(a) $R (x) = f (x) + g (x)$

(b) $R (x) = f (x) - g (x)$ :

$f (x) = \frac{- 4 x - 24}{x^{2} + x - 30} g (x) = \frac{x + 7}{5 - x}$

See all solutions

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