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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. 212 (page 694)

In the following exercises, solve each rational equation.
$\frac{2}{s + 7} - \frac{3}{s - 3} = 1$

Short Answer

Expert verified

The solution is $s = - 2, - 3$

Step by step solution

01

Step 1. Given

The given equation is: $\frac{2}{s + 7} - \frac{3}{s - 3} = 1$ .

02

Step 2. To find

We have to solve the equation.

03

Step 3. Calculation

We multiply both sides by the LCD, then solve the equation.

$\frac{2}{s + 7} - \frac{3}{s - 3} = 1 \frac{2}{s + 7} (s + 7) (s - 3) - \frac{3}{s - 3} (s + 7) (s - 3) = 1 (s + 7) (s - 3) 2 (s - 3) - 3 (s + 7) = (s + 7) (s - 3) 2 s - 6 - 3 s - 21 = s^{2} - 3 s + 7 s - 21 - s - 27 = s^{2} + 4 s - 21 s^{2} + 5 s + 6 = 0 (s + 2) (s + 3) = 0 s = - 2, - 3$

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Most popular questions from this chapter

In the following exercise, find

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

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

$f (x) = \frac{- 5 x - 5}{x^{2} + x - 6} g (x) = \frac{x + 1}{2 - x}$

In the following exercises, find the domain of each function.

$R (x) = \frac{3 x^{2} + 15 x}{6 x^{2} + 6 x - 36}$

Determine the values for which the rational expression is undefined.

$\frac{b - 7}{b^{2} - 25} .$

In the following exercise, perform the indicated operation:

$\frac{6 d}{d - 5} + \frac{1}{d + 4} - \frac{7 d - 5}{d^{2} - d - 20}$

For the following exercises, perform the indicated operations.

$\frac{4 n^{2} + 32 n}{3 n + 2} . \frac{3 n^{2} - n - 2}{n^{2} + n - 30} 梅 \frac{108 n^{2} - 24 n}{n + 6}$

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