Q. 7.78 Solve: 5x2+2x-3-3x2+x-2=1x2+5x+6... [FREE SOLUTION]

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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. 7.78 (page 690)

Solve: $\frac{5}{x^{2} + 2 x - 3} - \frac{3}{x^{2} + x - 2} = \frac{1}{x^{2} + 5 x + 6}$

Short Answer

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Step by step solution

Step 1. Given.

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

Step 2. To find

We have to solve the given equation.

Step 3. Calculation

$\frac{5}{x^{2} + 2 x - 3} - \frac{3}{x^{2} + x - 2} = \frac{1}{x^{2} + 5 x + 6} \frac{5}{(x + 3) (x - 1)} - \frac{3}{(x + 2) (x - 1)} = \frac{1}{(x + 2) (x + 3)} LCMofthedenominators = (x - 1) (x + 2) (x + 3) . So, x - 1 鈮� 0 or x 鈮� 1 And x + 2 鈮� 0 or x 鈮� - 2 And x + 3 鈮� 0 or x 鈮� - 3 Multiplybothsidesby (x - 1) (x + 2) (x + 3) . \frac{5}{(x + 3) (x - 1)} - \frac{3}{(x + 2) (x - 1)} = \frac{1}{(x + 2) (x + 3)} \frac{5}{(x + 3) (x - 1)} (x - 1) (x + 2) (x + 3) - \frac{3}{(x + 2) (x - 1)} (x - 1) (x + 2) (x + 3) = \frac{1}{(x + 2) (x + 3)} (x - 1) (x + 2) (x + 3) 5 (x + 2) - 3 (x + 3) = x - 1 5 x + 10 - 3 x - 9 = x - 1 2 x + 1 = x - 1 2 x - x = - 1 - 1 x = - 2 But, x 鈮� - 2 . Sothereisnosolution.$

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91影视

Solve: $\frac{5}{x^{2} + 2 x - 3} - \frac{3}{x^{2} + x - 2} = \frac{1}{x^{2} + 5 x + 6}$

Short Answer

Step by step solution

Step 1. Given.

Step 2. To find

Step 3. Calculation

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