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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. 553 (page 1026)

In the following exercises, find the LCD.
$\frac{5}{3 p^{2} + 19 p + 6}, \frac{2 p}{3 p^{2} + 25 p + 8}$

Short Answer

Expert verified

The LCD is $(3 p + 1) .$

Step by step solution

01

Step 1. Given Information.

The given expression is:

$\frac{5}{3 p^{2} + 19 p + 6}, \frac{2 p}{3 p^{2} + 25 p + 8}$

02

Step 2. Factorization.

$c o n s i d e r, 3 p^{2} + 19 p + 6 3 p^{2} + 18 p + p + 6 3 p (p + 6) + 1 (p + 6) (3 p + 1) (p + 6) N o w c o n s i d e r i n g t h e s e c o n d e x p r e s s i o n 3 p^{2} + 25 p + 8 3 p^{2} + 24 p + p + 8 3 p (p + 8) + 1 (p + 8) (3 p + 1) (p + 8) T h e e n t i r e e x p r e s s i o n b e c o m e s \frac{5}{(3 p + 1) (p + 6)}, \frac{2 p}{(3 p + 1) (p + 8)}$

03

Step 3. Finding LCD.

$\frac{5}{(3 p + 1) (p + 6)}, \frac{2 p}{(3 p + 1) (p + 8)} S i n c e b o t h t h e d e n o m i n a t o r s h a v e (3 p + 1) i t s L C D i s (3 p + 1) .$

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