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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 7: Q. 7.84 (page 693)

Solve: $\frac{2}{x} + \frac{1}{3} = \frac{1}{y}$ for $y .$

Short Answer

Expert verified

The solution is $y = \frac{3 x}{x + 6}$ .

Step by step solution

01

Step 1. Given

The given equation is: $\frac{2}{x} + \frac{1}{3} = \frac{1}{y}$ .

02

Step 2. To find

We have to solve the equation for y.

03

Step 3. Calculation

We will solve this problem using LCD.

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

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Solve each rational function inequality and write the solution in interval notation.

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