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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. 94 (page 667)

In the following exercises, add or subtract.
$\frac{6 y^{2} + 2 y - 11}{3 y - 7} + \frac{3 y^{2} - 3 y + 17}{7 - 3 y}$

Short Answer

Expert verified

The sum of the expressions is $x - 12$ .

Step by step solution

01

Step 1. Given Information

The given expression is $\frac{6 y^{2} + 2 y - 11}{3 y - 7} + \frac{3 y^{2} - 3 y + 17}{7 - 3 y}$

02

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

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

$\frac{6 y^{2} + 2 y - 11}{3 y - 7} + \frac{3 y^{2} - 3 y + 17}{7 - 3 y} = \frac{6 y^{2} + 2 y - 11}{3 y - 7} + \frac{- 3 y^{2} + 3 y - 17}{3 y - 7}$

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.

$\begin{array}{rcl} \frac{6 y^{2} + 2 y - 11}{3 y - 7} + \frac{- 3 y^{2} + 3 y - 17}{3 y - 7} & = & \frac{6 y^{2} + 2 y - 11 - 3 y^{2} + 3 y - 17}{3 y - 7} \\ = & \frac{3 y^{2} + 5 y - 28}{3 y - 7} \end{array}$

04

Step 4. Simplify

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

$\begin{array}{rcl} \frac{3 y^{2} + 5 y - 28}{3 y - 7} & = & \frac{(3 y - 7) (y - 12)}{3 y - 7} \\ = & y - 12 \end{array}$

So, the sum is $y - 12$ .

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