Chapter 7: Q. 417 (page 736)

In the following exercises, perform the indicated operations
$\frac{3 y}{y + 2} - \frac{y + 2}{y + 8}$

Short Answer

Expert verified

Simplified expression is $\frac{2 y^{2} + 20 y - 4}{(y + 2) (y + 8)}$

Step by step solution

Step 1. Given Information

Expression:

\frac{3 y}{y + 2} - \frac{y + 2}{y + 8}

Step 2. Find LCD

Denominator of first fraction is $(y + 2)$

Denominator of the second fraction is $(y + 8)$

here nothing is common between both denominator

So the LCD is $(y + 2) (y + 8)$

Step 3. Rewrite each rational expression as an equivalent rational expression with the LCD

$\frac{3 y (y + 8)}{(y + 2) (y + 8)} - \frac{(y + 2) (y + 2)}{(y + 2) (y + 8)}$

Step 4.Simplify the numerators.

$\frac{3 y^{2} + 24 y}{(y + 2) (y + 8)} - \frac{{(y + 2)}^{2}}{(y + 2) (y + 8)} = \frac{3 y^{2} + 24 y}{(y + 2) (y + 8)} - \frac{y^{2} + 4 y + 4}{(y + 2) (y + 8)}$

Step 5. Subtract numerators

$\frac{3 y^{2} + 24 y - (y^{2} + 4 y + 4)}{(y + 2) (y + 8)}$

Step 6. Simplify numerator

$\frac{3 y^{2} + 24 y - y^{2} - 4 y - 4}{(y + 2) (y + 8)} = \frac{2 y^{2} + 20 y - 4}{(y + 2) (y + 8)}$

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In the following exercises, perform the indicated operations
$\frac{3 y}{y + 2} - \frac{y + 2}{y + 8}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Find LCD

Step 3. Rewrite each rational expression as an equivalent rational expression with the LCD

Step 4.Simplify the numerators.

Step 5. Subtract numerators

Step 6. Simplify numerator

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In the following exercises, perform the indicated operations 3yy+2-y+2y+8

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Find LCD

Step 3. Rewrite each rational expression as an equivalent rational expression with the LCD

Step 4.Simplify the numerators.

Step 5. Subtract numerators

Step 6. Simplify numerator

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Probability and Statistics

Applied Mathematics

Geometry

Decision Maths

Calculus

Study anywhere. Anytime. Across all devices.

In the following exercises, perform the indicated operations
$\frac{3 y}{y + 2} - \frac{y + 2}{y + 8}$