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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. 229 (page 695)

In the following exercises, solve each rational equation.
$\frac{3}{x^{2} - 5 x - 6} + \frac{3}{x^{2} - 7 x + 6} = \frac{6}{x^{2} - 1}$

Short Answer

Expert verified

There is no solution.

Step by step solution

01

Step 1. Given

The given equation is: $\frac{3}{x^{2} - 5 x - 6} + \frac{3}{x^{2} - 7 x + 6} = \frac{6}{x^{2} - 1}$ .

02

Step 2. To find

We have to solve the equation.

03

Step 3. Calculation

Factor the denominators.

$\frac{3}{x^{2} - 5 x - 6} + \frac{3}{x^{2} - 7 x + 6} = \frac{6}{x^{2} - 1} \frac{3}{(x - 6) (x + 1)} + \frac{3}{(x - 6) (x - 1)} = \frac{6}{(x + 1) (x - 1)}$

The denominator is never 0. So, $x 鈮� 6, - 1, 1$ .

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

$\frac{3}{(x - 6) (x + 1)} + \frac{3}{(x - 6) (x - 1)} = \frac{6}{(x + 1) (x - 1)} \frac{3}{(x - 6) (x + 1)} (x - 6) (x + 1) (x - 1) + \frac{3}{(x - 6) (x - 1)} (x - 6) (x + 1) (x - 1) = \frac{6}{(x + 1) (x - 1)} (x - 6) (x + 1) (x - 1) 3 (x - 1) + 3 (x + 1) = 6 (x - 6) 3 x - 3 + 3 x + 3 = 6 x - 36 6 x = 6 x - 36 0 = - 36$

This is not possible. So there is no solution.

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