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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. 7.77 (page 690)

Solve: $\frac{15}{x^{2} + x - 6} - \frac{3}{x - 2} = \frac{2}{x + 3} .$

Short Answer

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Step by step solution

01

Step 1. Given.

The given equation is: $\frac{15}{x^{2} + x - 6} - \frac{3}{x - 2} = \frac{2}{x + 3} .$

02

Step 2. To find

We have to solve the given equation.

03

Step 3. Calculation

$\frac{15}{x^{2} + x - 6} - \frac{3}{x - 2} = \frac{2}{x + 3} \frac{15}{(x - 2) (x + 3)} - \frac{3}{x - 2} = \frac{2}{x + 3} LCMofthedenominators = (x - 2) (x + 3) . So, x - 2 鈮� 0 or x 鈮� 2 And x + 3 鈮� 0 or x 鈮� - 3 Multiplybothsidesby (x - 2) (x + 3) . \frac{15}{(x - 2) (x + 3)} (x - 2) (x + 3) - \frac{3}{x - 2} (x - 2) (x + 3) = \frac{2}{x + 3} (x - 2) (x + 3) 15 - 3 (x + 3) = 2 (x - 2) 15 - 3 x - 9 = 2 x - 4 - 3 x + 6 = 2 x - 4 2 x + 3 x = 6 + 4 5 x = 10 x = 2 But, x 鈮� 2 . Sothereisnosolution.$

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