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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. 12 (page 651)

Simplify the rational expression $\frac{y^{2} + 3 y - 4}{y^{2} - 6 y + 5}$

Short Answer

Expert verified

Simplified form of s rational expression $\frac{y^{2} + 3 y - 4}{y^{2} - 6 y + 5} i s \frac{(y + 4)}{(y - 5)}, y 鈮� 5 .$

Step by step solution

01

Step 1. Given expression

Given rational expression is $\frac{y^{2} + 3 y - 4}{y^{2} - 6 y + 5}$ .

We have to simplify the given rational expression.

02

Step 2. Simplification of the rational expression

To simplify the given rational expression ,first factor numerator and denominators separately and then divide out the common factor.

Then the simplified form of expression is $\frac{y^{2} + 3 y - 4}{y^{2} - 6 y + 5} = \frac{(y + 4) (y - 1)}{(y - 5) (y - 1)} = \frac{(y - 4)}{(y - 5)}; y 鈮� 5 \sin c e (y - 1) i s t h e c o m m o n f a c t o r .$

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Most popular questions from this chapter

In the following exercises, divide the rational expressions.

$\frac{v - 5}{11 - v} 梅 \frac{v^{2} - 25}{v - 11}$

In the following exercise, find

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

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

role="math" localid="1644749808906" $f (x) = \frac{5}{x + 7} g (x) = \frac{10 x}{x^{2} - 49}$

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

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

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

$f (x) = \frac{4 x}{x^{2} - 3 x - 10} a n d g (x) = \frac{x^{2} - 25}{8 x^{2}}$

Simplify the complex rational expression by writing it as division:

$\frac{\frac{3}{4} - \frac{1}{3}}{\frac{1}{8} + \frac{5}{6}}$

See all solutions

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