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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. 80 (page 667)

In the following exercises, add.
$\frac{3 s^{2}}{3 s - 2} + \frac{13 s - 10}{3 s - 2}$

Short Answer

Expert verified

The simplified expression is $s + 5$ but $s 鈮� \frac{2}{3}$ .

Step by step solution

01

Step 1. Given Information

The given expression is $\frac{3 s^{2}}{3 s - 2} + \frac{13 s - 10}{3 s - 2}$ .

02

Step 2. Add the numerator

As the denominator is the same for both the terms, add the numerator and place it over the common denominator.

$\frac{3 s^{2}}{3 s - 2} + \frac{13 s - 10}{3 s - 2} = \frac{3 s^{2} + 13 s - 10}{3 s - 2}$

03

Step 3. Factor the numerator

Factor the expression in the numerator and then cancel out the common terms from the numerator and denominator.

$\frac{(3 s - 2) (s + 5)}{(3 s - 2)} = s + 5$

So, the resultant expression is $s + 5$ but the denominator of the given expression was $3 s - 2$ , so, $s 鈮� \frac{2}{3}$ .

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Most popular questions from this chapter

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

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

Multiply $\frac{72 x - 12 x^{2}}{8 x + 32} . \frac{x^{2} + 10 x + 24}{x^{2} - 36}$

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 a division:

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In the following exercises, solve each rational inequality and write the solution in interval notation.

$\frac{5}{(x - 1)} 鈮� \frac{4}{(x + 2)}$

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