Chapter 8: Q. 298 (page 967)

Simplify
In the following exercises, use either method.
$\frac{\frac{y}{y + 3}}{2 + \frac{1}{y - 3}}$ .

Short Answer

Expert verified

The simplified expression for $\frac{\frac{y}{y + 3}}{2 + \frac{1}{y - 3}}$ is, $\frac{y^{2} - 3 y}{(y + 3) (2 y - 5)}$ .

Step by step solution

Step 1. Given information

$\frac{\frac{y}{y + 3}}{2 + \frac{1}{y - 3}}$ .

We need to simplify the given expression.

Step 2.Find the LCD of all fractions in the complex rational expression.

The LCD is, $(y + 3) (y - 3)$ .

Multiply the numerator and the denominator by the LCD.

$\frac{\frac{y}{y + 3}}{2 + \frac{1}{y - 3}} = \frac{(y + 3) (y - 3) \frac{y}{y + 3}}{(y + 3) (y - 3) (2 + \frac{1}{y - 3})}$

Distribute the LCD in the denominator and then simplify.

$\frac{(y + 3) (y - 3) \frac{y}{y + 3}}{(y + 3) (y - 3) (2 + \frac{1}{y - 3})} = \frac{(y + 3) (y - 3) \frac{y}{y + 3}}{(2 (y + 3) (y - 3) + (y + 3) (y - 3) . \frac{1}{y - 3})}$

Step 3. Now simplify the obtained expression.

$\frac{(y + 3) (y - 3) \frac{y}{y + 3}}{(2 (y + 3) (y - 3) + (y + 3) (y - 3) . \frac{1}{y - 3})} = \frac{(y - 3) y}{(2 (y + 3) (y - 3) + (y + 3))} = \frac{y (y - 3)}{2 (y^{2} - 9) + (y + 3)} = \frac{y (y - 3)}{2 y^{2} - 18 + y + 3} = \frac{y (y - 3)}{2 y^{2} + y - 15} = \frac{y^{2} - 3 y}{(y + 3) (2 y - 5)}$

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Simplify
In the following exercises, use either method.
$\frac{\frac{y}{y + 3}}{2 + \frac{1}{y - 3}}$ .

Short Answer

Step by step solution

Step 1. Given information

Step 2.Find the LCD of all fractions in the complex rational expression.

Step 3. Now simplify the obtained expression.

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SimplifyIn the following exercises, use either method.yy+32+1y-3.

Short Answer

Step by step solution

Step 1. Given information

Step 2.Find the LCD of all fractions in the complex rational expression.

Step 3. Now simplify the obtained expression.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Theoretical and Mathematical Physics

Probability and Statistics

Statistics

Pure Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Simplify
In the following exercises, use either method.
$\frac{\frac{y}{y + 3}}{2 + \frac{1}{y - 3}}$ .