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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

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

01

Step 1. Given expression

Expression

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

It can be rewritten as

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

02

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 $(m + 2) (1) = m + 2$

03

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

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

04

Step 4.Simplify the numerators.

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

05

Step 5. Subtract numerators

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

06

Step 6. Simplify numerator

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

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Most popular questions from this chapter

Use the Quotient Property to simplify square roots.

(a) $\frac{\sqrt{50 m^{7}}}{\sqrt{2 m}}$

(b) $\sqrt[3]{\frac{1250}{2}}$

(c) $\sqrt[4]{\frac{486 y^{9}}{2 y^{3}}}$

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Divide: $\frac{1 + 6 i}{6 - i}$

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