Q. 228 In the following exercises, solv... [FREE SOLUTION]

91影视

Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q. 228 (page 695)

In the following exercises, solve each rational equation.
$\frac{5}{x^{2} + 4 x + 3} + \frac{2}{x^{2} + x - 6} = \frac{3}{x^{2} - x - 2}$ .

Short Answer

Expert verified

The solution is $x = \frac{17}{4}$

Step by step solution

Step 1. Given

The given equation is: $\frac{5}{x^{2} + 4 x + 3} + \frac{2}{x^{2} + x - 6} = \frac{3}{x^{2} - x - 2}$ .

Step 2. To find

We have to solve the equation.

Step 3. Calculation

Factor the denominators.

$\frac{5}{x^{2} + 4 x + 3} + \frac{2}{x^{2} + x - 6} = \frac{3}{x^{2} - x - 2} \frac{5}{(x + 3) (x + 1)} + \frac{2}{(x + 3) (x - 2)} = \frac{3}{(x - 2) (x + 1)}$

The denominator is never 0. So, $x 鈮� - 3, - 1, 2$ .

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

$\frac{5}{(x + 3) (x + 1)} + \frac{2}{(x + 3) (x - 2)} = \frac{3}{(x - 2) (x + 1)} \frac{5}{(x + 3) (x + 1)} (x + 3) (x + 1) (x - 2) + \frac{2}{(x + 3) (x - 2)} (x + 3) (x + 1) (x - 2) = \frac{3}{(x - 2) (x + 1)} (x + 3) (x + 1) (x - 2) 5 (x - 2) + 2 (x + 1) = 3 (x + 3) 5 x - 10 + 2 x + 2 = 3 x + 9 7 x - 8 = 3 x + 9 7 x - 3 x = 9 + 8 4 x = 17 x = \frac{17}{4}$

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91影视

In the following exercises, solve each rational equation.
$\frac{5}{x^{2} + 4 x + 3} + \frac{2}{x^{2} + x - 6} = \frac{3}{x^{2} - x - 2}$ .

Short Answer

Step by step solution

Step 1. Given

Step 2. To find

Step 3. Calculation

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91影视

In the following exercises, solve each rational equation.5x2+4x+3+2x2+x-6=3x2-x-2.

Short Answer

Step by step solution

Step 1. Given

Step 2. To find

Step 3. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Calculus

Pure Maths

Mechanics Maths

Statistics

Geometry

Study anywhere. Anytime. Across all devices.

In the following exercises, solve each rational equation.
$\frac{5}{x^{2} + 4 x + 3} + \frac{2}{x^{2} + x - 6} = \frac{3}{x^{2} - x - 2}$ .