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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q. 249 (page 695)

Solve the rational equation $\frac{3}{x} - \frac{5}{y} = \frac{1}{4}$ for the variable y.

Short Answer

Expert verified

The required equation is $y = \frac{20 x}{12 - x}$ .

Step by step solution

01

Given information

The equation is given as $\frac{3}{x} - \frac{5}{y} = \frac{1}{4}$ to find the expression for y.

02

Solve the given equation

Apply the given equation to find the required expression.

Add $\frac{5}{y}$ and subtract $\frac{1}{4}$ into both sides of the given equation.
Take the least common multiple on the left side of the equation.
Solve the obtained equation for y.

$\begin{array}{rcl} \frac{3}{x} - \frac{5}{y} & = & \frac{1}{4} \\ \frac{3}{x} - \frac{5}{y} + \frac{5}{y} - \frac{1}{4} & = & \frac{1}{4} + \frac{5}{y} - \frac{1}{4} \\ \frac{3}{x} - \frac{1}{4} & = & \frac{5}{y} . . . . . . . . . . . . . . . . . . (1) \\ \frac{3 脳 4 - 1 脳 x}{4 x} & = & \frac{5}{y} \\ \frac{12 - x}{4 x} & = & \frac{5}{y} \\ \frac{4 x}{12 - x} & = & \frac{y}{5} \\ y & = & \frac{4 x 脳 5}{12 - x} \\ y & = & \frac{20 x}{12 - x} \end{array}$

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Most popular questions from this chapter

Write the steps you would use to explain solving rational inequalities to your little brother.

In the following exercises, divide the rational expressions.

$\frac{v - 5}{11 - v} 梅 \frac{v^{2} - 25}{v - 11}$

In the following exercises, find the domain of each function.

$R (x) = \frac{8 x^{2} - 32 x}{2 x^{2} - 6 x - 80}$

Divide $\frac{y^{2} - 16}{4} 梅 \frac{y^{3} - 64}{2 y^{2} + 8 y + 32}$

In the following exercises, solve each rational inequality and write the solution in interval notation.

$\frac{5}{(x - 1)} 鈮� \frac{4}{(x + 2)}$

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