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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 5: Q.339. (page 552)

Divide $\frac{10 x^{2} + x - 12}{2 x}$ and explain with words how you get each term of the quotient.

Short Answer

Expert verified

The solution is $5 x + \frac{1}{2} - \frac{6}{x}$ .

Step by step solution

01

Step 1. Given information.

The given expression is $\frac{10 x^{2} + x - 12}{2 x}$ .

02

Step 2. Separating each terms.

$\frac{10 x^{2} + x - 12}{2 x} = \frac{10 x^{2}}{2 x} + \frac{x}{2 x} - \frac{12}{2 x}$

03

Step 3. Simplify the expression.

Using quotient property, $\frac{a^{m}}{a^{n}} = a^{m - n}$ , where $a$ is not equal to zero.

$鈬� \frac{10}{2} x^{2 - 1} + \frac{x}{2 x} - \frac{12}{2 x} 鈬� 5 x + \frac{1}{2} - \frac{6}{x}$

04

Step 4. Simplified answer.

Hence, the simplified expression is $5 x + \frac{1}{2} - \frac{6}{x}$ .

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