Chapter 11: Q. 230 (page 1069)

In the following exercises, solve each rational equation.
$\frac{2}{x^{2} + 2 x - 3} + \frac{3}{x^{2} + 4 x + 3} = \frac{6}{x^{2} - 1}$

Short Answer

Expert verified

The solution is $x = - 19$ .

Step by step solution

Step 1. Given

The given equation is: $\frac{2}{x^{2} + 2 x - 3} + \frac{3}{x^{2} + 4 x + 3} = \frac{6}{x^{2} - 1}$

Step 2. To find

We have to solve the equation.

Step 3. Calculation

Factor the denominators.

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

The denominator is never 0. So, $x \neq - 3, 1, - 1$ ..

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

localid="1662465746915" $\frac{2}{(x + 3) (x - 1)} + \frac{3}{(x + 3) (x + 1)} = \frac{6}{(x + 1) (x - 1)} \frac{2}{(x + 3) (x - 1)} (x + 3) (x - 1) (x + 1) + \frac{3}{(x + 3) (x + 1)} (x + 3) (x - 1) (x + 1) = \frac{6}{(x + 1) (x - 1)} (x + 3) (x - 1) (x + 1) 2 (x + 1) + 3 (x - 1) = 6 (x + 3) 2 x + 2 + 3 x - 3 = 6 x + 18 5 x - 1 = 6 x + 18 - x = 19 x = - 19$

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In the following exercises, solve each rational equation.
$\frac{2}{x^{2} + 2 x - 3} + \frac{3}{x^{2} + 4 x + 3} = \frac{6}{x^{2} - 1}$

Short Answer

Step by step solution

Step 1. Given

Step 2. To find

Step 3. Calculation

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In the following exercises, solve each rational equation.2x2+2x-3+3x2+4x+3=6x2-1

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

Logic and Functions

Decision Maths

Statistics

Mechanics Maths

Applied Mathematics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

In the following exercises, solve each rational equation.
$\frac{2}{x^{2} + 2 x - 3} + \frac{3}{x^{2} + 4 x + 3} = \frac{6}{x^{2} - 1}$