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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 8: Q 8.72 (page 938)

Add $\frac{6 y^{2} + 7 y - 10}{4 y - 7} + \frac{2 y^{2} + 2 y + 11}{7 - 4 y}$ .

Short Answer

Expert verified

The required expression is $y + 3 .$

Step by step solution

01

Given information

The given expression is

$\frac{6 y^{2} + 7 y - 10}{4 y - 7} + \frac{2 y^{2} + 2 y + 11}{7 - 4 y}$

02

Simplifying the expression

The denominators of the two expressions are opposite to each other, so multiply the second rational expression with $\frac{6 y^{2} + 7 y - 10}{4 y - 7} + \frac{(- 1) (2 y^{2} + 2 y + 11)}{(- 1) (7 - 4 y)}$

Simplifying the second expression:

$\frac{6 y^{2} + 7 y - 10}{4 y - 7} + \frac{- 2 y^{2} - 2 y - 11}{4 y - 7}$

Combine like terms:

Factor the numerator:

$\frac{(4 y - 7) (y + 3)}{4 y - 7}$

Cancel the like factors from numerator and denominator:

$y + 3 .$

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