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

Given information

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

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.

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

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

Short Answer

Step by step solution

Given information

Solve the given equation

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Solve the rational equation3x-5y=14for the variable y.

Short Answer

Step by step solution

Given information

Solve the given equation

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