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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 159 (page 940)

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

Short Answer

Expert verified

The required expression is $x + 2$ .

Step by step solution

01

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

Simplifying the expression

The denominators of two expressions are opposite, multiply the second expression with $\frac{- 1}{- 1} :$

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

Combining the like terms after distributing negative sign in second expression:

$\frac{8 x^{2} + 13 x - 6}{8 x - 3}$

Factorizing the numerator:

$\frac{(8 x - 3) (x + 2)}{8 x - 3}$

Cancelling the common term from numerator and denominator:

$x + 2$

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