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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 170 (page 953)

Find the LCD of $\frac{8}{y^{2} + 12 y + 35}, \frac{3 y}{y^{2} + y - 42}$ .

Short Answer

Expert verified

The LCD is $y^{3} + 6 y^{2} - 37 y - 210$ .

Step by step solution

01

Given Information

The given expression is $\frac{8}{y^{2} + 12 y + 35}, \frac{3 y}{y^{2} + y - 42}$ .

02

Factor the denominator of both expressions.

The factored form of first denominator.

$y^{2} + 12 y + 35 = (y + 5) (y + 7)$

The factored form of second denominator.

$y^{2} + y - 42 = (y - 6) (y + 7)$

03

Determine the common factors and from the remaining factors, multiply each of the denominator with appropriate factors.

The common factor is $(y + 7)$ .

Multiply common factor with other factors.

$= y^{3} + 6 y^{2} - 37 y - 210$

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