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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. 354 (page 983)

In the following exercises, solve.
$\frac{6}{x} + \frac{2}{3} = \frac{1}{y} f o r y$

Short Answer

Expert verified

The solution is $y = \frac{3 x}{18 + 2 x} .$

Step by step solution

01

Step 1. Given Information.

The given equation is $\frac{6}{x} + \frac{2}{3} = \frac{1}{y} f o r y .$

02

Step 2. Solve

To solve the equation, clear the fractions by multiplying both sides of the equations by the LCD, $3 x$

$(3 x) (\frac{6}{x} + \frac{2}{3}) = (\frac{1}{y}) (3 x) (3 x) (\frac{18 + 2 x}{3 x}) = \frac{3 x}{y} 18 + 2 x = \frac{3 x}{y}$

Again remove the fractions by multiplying both sides of the equation by y

$(y) 脳 (18 + 2 x) = (\frac{3 x}{y}) 脳 y 18 y + 2 x y = 3 x y (18 + 2 x) = 3 x$

Now, divide both sides by $18 + 2 x$ to isolate y

$\frac{y (18 + 2 x)}{18 + 2 x} = \frac{3 x}{18 + 2 x} y = \frac{3 x}{18 + 2 x}$

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