Chapter 7: Q. 7.62 (page 678)

Simplify the complex rational expression by using the LCD:
$\frac{\frac{4 y}{y + 5} + \frac{2}{y + 6}}{\frac{3 y}{y^{2} + 11 y + 30}}$

Short Answer

Expert verified

The simplified expression is $\frac{(2 y^{2} + 13 y + 5)}{3 y}$ .

Step by step solution

Step 1. Given Information.

We have:

$\frac{\frac{4 y}{y + 5} + \frac{2}{y + 6}}{\frac{3 y}{y^{2} + 11 y + 30}}$

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

The least common divisor is $(y + 5) (y + 6)$ .

Multiply the numerator and denominator by the LCD:

$= \frac{(y + 5) (y + 6) (\frac{4 y}{y + 5} + \frac{2}{y + 6})}{(y + 5) (y + 6) (\frac{3 y}{y^{2} + 11 y + 30})}$

Step 3. Simplify the expression.

Further, calculate:

$= \frac{(y + 5) (y + 6) (\frac{4 y}{(y + 5)} + \frac{2}{(y + 6)})}{(y + 5) (y + 6) (\frac{3 y}{y^{2} + 5 y + 6 y + 30})} = \frac{(y + 5) (y + 6) (\frac{4 y (y + 6) + 2 (y + 5)}{(y + 5) (y + 6)})}{(y + 5) (y + 6) (\frac{3 y}{y (y + 5) + 6 (y + 5)})} = \frac{(y + 5) (y + 6) (\frac{4 y^{2} + 24 y + 4 y + 10}{(y + 5) (y + 6)})}{(y + 5) (y + 6) (\frac{3 y}{(y + 5) (y + 6)})} = \frac{4 y^{2} + 26 y + 10}{3 y} = \frac{2 (2 y^{2} + 13 y + 5)}{3 y}$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Simplify the complex rational expression by using the LCD:
$\frac{\frac{4 y}{y + 5} + \frac{2}{y + 6}}{\frac{3 y}{y^{2} + 11 y + 30}}$

Short Answer

Step by step solution

Step 1. Given Information.

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

Step 3. Simplify the expression.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Applied Mathematics

Decision Maths

Pure Maths

Probability and Statistics

Geometry

Study anywhere. Anytime. Across all devices.

Simplify the complex rational expression by using the LCD:4yy+5+2y+63yy2+11y+30

Short Answer

Step by step solution

Step 1. Given Information.

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

Step 3. Simplify the expression.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Applied Mathematics

Decision Maths

Pure Maths

Probability and Statistics

Geometry

Study anywhere. Anytime. Across all devices.

Simplify the complex rational expression by using the LCD:
$\frac{\frac{4 y}{y + 5} + \frac{2}{y + 6}}{\frac{3 y}{y^{2} + 11 y + 30}}$