Chapter 1: Q. 35 (page 29)

In Problem 17-36, solve each equation algebraically. Verify your solution using a graphing utility.
$\frac{2}{x + 2} + \frac{3}{x - 1} = - \frac{8}{5}$

Short Answer

Expert verified

The required solutions are $x = - 4, x = - \frac{1}{8}$ and the graph of the function is shown below:

Step by step solution

Step 1. Given information.

We have:

$\frac{2}{x + 2} + \frac{3}{x - 1} = - \frac{8}{5}$

Step 2. Simplify the equation.

The equation is $\frac{2}{x + 2} + \frac{3}{x - 1} = - \frac{8}{5}$ .

Multiply both sides by LCM (least common multiple): $(x + 2) (x - 1)$

$(x + 2) (x - 1) \frac{2}{x + 2} + (x + 2) (x - 1) \frac{3}{x - 1} = (x + 2) (x - 1) - \frac{8}{5} 10 (x - 1) + 15 (x + 2) = - 8 (x + 2) (x - 1) 10 x - 10 + 15 x + 30 = - 8 (x^{2} + x - 2) 25 x + 20 = - 8 x^{2} - 8 x + 16 25 x + 20 + 8 x^{2} + 8 x - 16 = 0 8 x^{2} + 33 x + 4 = 0$

Step 3. Solve the equation by quadratic formula.

For a quadratic equation of the form $a x^{2} + b x + c = 0$ , the solutions are:

$x_{1, 2} = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$

For $a = 8, b = 33, c = 4$

$x_{1, 2} = \frac{- 33 \pm \sqrt{33^{2} - 4 \cdot 8 \cdot 4}}{2 \cdot 8} x_{1, 2} = \frac{- 33 \pm 31}{2 \cdot 8} x = - \frac{1}{8}, x = - 4$

Step 3. Verify the solution using a graphing utility.

The solution of the equation is $x = - \frac{1}{8}, x = - 4$ .

Draw the graph of the equation $\frac{2}{x + 2} + \frac{3}{x - 1} = - \frac{8}{5}$ using graphing utility:

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In Problem 17-36, solve each equation algebraically. Verify your solution using a graphing utility.
$\frac{2}{x + 2} + \frac{3}{x - 1} = - \frac{8}{5}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the equation.

Step 3. Solve the equation by quadratic formula.

Step 3. Verify the solution using a graphing utility.

One App. One Place for Learning.

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In Problem 17-36, solve each equation algebraically. Verify your solution using a graphing utility.2x+2+3x-1=-85

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the equation.

Step 3. Solve the equation by quadratic formula.

Step 3. Verify the solution using a graphing utility.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Logic and Functions

Statistics

Probability and Statistics

Geometry

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In Problem 17-36, solve each equation algebraically. Verify your solution using a graphing utility.
$\frac{2}{x + 2} + \frac{3}{x - 1} = - \frac{8}{5}$