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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. 357 (page 983)

In the following exercises, solve.
$\frac{3}{x} - \frac{5}{y} = \frac{1}{4} f o r y$

Short Answer

Expert verified

The solution is $y = \frac{x y + 20 x}{12} .$

Step by step solution

01

Step 1. Given Information.

The given equation is $\frac{3}{x} - \frac{5}{y} = \frac{1}{4} f o r y .$

02

Step 2. Solve

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

$(x y) (\frac{3}{x} - \frac{5}{y}) = \frac{1}{4} (x y) (x y) (\frac{3 y - 5 x}{x y}) = \frac{x y}{4} 3 y - 5 x = \frac{x y}{4} 3 y = \frac{x y}{4} + 5 x 3 y = \frac{x y + 20 x}{4}$

Now, divide both sides by $3$ to isolate y

$\frac{3 y}{3} = \frac{\frac{x y + 20 x}{4}}{3} y = \frac{x y + 20 x}{12}$

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