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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. 216 (page 694)

In the following exercises, solve each rational equation.
$\frac{y - 5}{y^{2} - 4 y - 5} = \frac{1}{y + 1} + \frac{1}{y - 5}$ .

Short Answer

Expert verified

There is no solution.

Step by step solution

01

Step 1. Given

The given equation is: $\frac{y - 5}{y^{2} - 4 y - 5} = \frac{1}{y + 1} + \frac{1}{y - 5}$ .

02

Step 2. To find

We have to solve the equation.

03

Step 3. Calculation

The denominators can never be 0. So, $y 鈮� - 1, 5$ .

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

$\frac{y - 5}{y^{2} - 4 y - 5} = \frac{1}{y + 1} + \frac{1}{y - 5} \frac{y - 5}{(y + 1) (y - 5)} = \frac{1}{y + 1} + \frac{1}{y - 5} \frac{y - 5}{(y + 1) (y - 5)} (y + 1) (y - 5) = \frac{1}{y + 1} (y + 1) (y - 5) + \frac{1}{y - 5} (y + 1) (y - 5) y - 5 = y - 5 + y + 1 y - 5 = 2 y - 4 y - 2 y = 5 - 4 - y = 1 y = - 1$

But $y = - 1$ . Hence, there is no solution.

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