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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. 7.70 (page 686)

Solve: $\frac{5}{y + 3} + \frac{2}{y - 3} = \frac{5}{y^{2} - 9}$ .

Short Answer

Expert verified

The solution is $y = 2$ .

Step by step solution

01

Step 1. Given.

The given equation is: $\frac{5}{y + 3} + \frac{2}{y - 3} = \frac{5}{y^{2} - 9}$

02

Step 2. To find

We have to solve the given equation.

03

Step 3. Calculation

The LCD is $(y + 3) (y - 3)$ . Multiply both sides of the equation by LCD. Then we solve the linear equation.

$\frac{5}{y + 3} + \frac{2}{y - 3} = \frac{5}{y^{2} - 9} \frac{5}{y + 3} (y + 3) (y - 3) + \frac{2}{y - 3} (y + 3) (y - 3) = \frac{5}{y^{2} - 9} (y + 3) (y - 3) 5 (y - 3) + 2 (y + 3) = 5 5 y - 15 + 2 y + 6 = 5 7 y - 9 = 5 7 y = 5 + 9 7 y = 14 y = \frac{14}{7} y = 2$

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