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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. 8.133 (page 979)

Solve :
$\frac{y}{5 y - 10} - \frac{5}{3 y + 6} = \frac{2 y^{2} - 19 y + 54}{15 y^{2} - 60}$ .

Short Answer

Expert verified

$y = 2, - 2$ .

Step by step solution

01

Step 1. Given information.

To solve $\frac{y}{5 y - 10} - \frac{5}{3 y + 6} = \frac{2 y^{2} - 19 y + 54}{15 y^{2} - 60}$ .

02

Step 2. Solve using LCD.

We have

$\frac{y}{5 y - 10} - \frac{5}{3 y + 6} = \frac{2 y^{2} - 19 y + 54}{15 y^{2} - 60} \frac{y}{5 y - 10} - \frac{5}{3 y + 6} = \frac{2 y^{2} - 19 y + 54}{(5 y - 10) (3 y + 6)}; y 鈮� \frac{10}{3}, - \frac{6}{3}$

Take LCD and multiply it to both sides,

$(5 y - 10) (3 y + 6) [\frac{y}{5 y - 10} - \frac{5}{3 y + 6}] = [\frac{2 y^{2} - 19 y + 54}{(5 y - 10) (3 y + 6)}] (5 y - 10) (3 y + 6) y (3 y + 6) - 5 (5 y - 10) = 2 y^{2} - 19 y + 54 3 y^{2} + 6 y - 25 y + 50 = 2 y^{2} - 19 y + 54 3 y^{2} - 19 y + 50 - 2 y^{2} + 19 y - 54 = 0 y^{2} - 4 = 0 y^{2} = 4 y = 卤 \sqrt{4} y = 卤 2$

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