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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q. 93 (page 667)

In the following exercises, add or subtract.
$\frac{10 x^{2} + 16 x - 7}{8 x - 3} + \frac{2 x^{2} + 3 x - 1}{3 - 8 x}$

Short Answer

Expert verified

The sum of the expressions is $x + 2$ .

Step by step solution

01

Step 1. Given Information

The given expression is $\frac{10 x^{2} + 16 x - 7}{8 x - 3} + \frac{2 x^{2} + 3 x - 1}{3 - 8 x}$ .

02

Step 2. Multiply Numerator and denominator of the second fraction by -1

Multiply the numerator and denominator of the second term by $- 1$ .

$\frac{10 x^{2} + 16 x - 7}{8 x - 3} + \frac{2 x^{2} + 3 x - 1}{3 - 8 x} = \frac{10 x^{2} + 16 x - 7}{8 x - 3} + \frac{- 2 x^{2} - 3 x + 1}{8 x - 3}$

03

Step 3. Add the Numerator

As the denominator is same for both the terms, add the numerator and place over the common denominator.
Add the like terms of the numerator.

$\begin{array}{rcl} \frac{10 x^{2} + 16 x - 7}{8 x - 3} + \frac{- 2 x^{2} - 3 x + 1}{8 x - 3} & = & \frac{10 x^{2} + 16 x - 7 - 2 x^{2} - 3 x + 1}{8 x - 3} \\ = & \frac{8 x^{2} + 13 x - 6}{8 x - 3} \end{array}$

04

Step 4. Simplify

Factor the expression in the numerator and then cancel out the common terms in numerator and denominator.

$\begin{array}{rcl} \frac{8 x^{2} + 13 x - 6}{8 x - 3} & = & \frac{(8 x - 3) (x + 2)}{8 x - 3} \\ = & x + 2 \end{array}$

So, the sum is $x + 2$ .

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