Chapter 11: Q. 419 (page 1069)

In the following exercises, perform the indicated operations
$\frac{7 m + 3}{m + 2} - 5$

Short Answer

Expert verified

Simplified expression is $\frac{2 m - 7}{m + 2}$

Step by step solution

Step 1. Given expression

Expression

\frac{7 m + 3}{m + 2} - 5

It can be rewritten as

$\frac{7 m + 3}{m + 2} - \frac{5}{1}$

Step 2. Find LCD

Denominator of the first fraction is $m + 2$

Denominator of the second fraction is 1

here nothing is common

So LCD is $(m + 2) (1) = m + 2$

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

$\frac{7 m + 3}{m + 2} - \frac{5 (m + 2)}{m + 2}$

Step 4.Simplify the numerators.

$\frac{7 m + 3}{m + 2} - \frac{5 m + 10}{m + 2}$

Step 5. Subtract numerators

$\frac{(7 m + 3) - (5 m + 10)}{m + 2}$

Step 6. Simplify numerator

$\frac{7 m + 3 - 5 m - 10}{m + 2} = \frac{2 m - 7}{m + 2}$

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.

In the following exercises, perform the indicated operations
$\frac{7 m + 3}{m + 2} - 5$

Short Answer

Step by step solution

Step 1. Given expression

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

Probability and Statistics

Mechanics Maths

Logic and Functions

Calculus

Applied Mathematics

Decision Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, perform the indicated operations 7m+3m+2-5

Short Answer

Step by step solution

Step 1. Given expression

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

Probability and Statistics

Mechanics Maths

Logic and Functions

Calculus

Applied Mathematics

Decision Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, perform the indicated operations
$\frac{7 m + 3}{m + 2} - 5$