Question

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

Short answer

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

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.

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