Solve x/y/frac{x{a}}=1

$$\frac { \frac { x } { y } } { \frac { x } { a } } = 1$$

Solve for a

$$a=y$$

$$y\neq 0\text{ and }x\neq 0$$

Solution Steps

Variable a cannot be equal to 0 since division by zero is not defined. Divide \frac{x}{y} by \frac{x}{a} by multiplying \frac{x}{y} by the reciprocal of \frac{x}{a}.

$$\frac{xa}{yx}=1$$

Cancel out x in both numerator and denominator.

$$\frac{a}{y}=1$$

Multiply both sides of the equation by y.

$$a=y$$

Variable a cannot be equal to 0.

$$a=y\text{, }a\neq 0$$

Solve for x

$$x\neq 0$$

$$y=a\text{ and }x\neq 0\text{ and }a\neq 0$$

Steps for Solving Linear Equation

Divide \frac{x}{y} by \frac{x}{a} by multiplying \frac{x}{y} by the reciprocal of \frac{x}{a}.

$$\frac{xa}{yx}=1$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by xy.

$$xa=xy$$

Subtract xy from both sides.

$$xa-xy=0$$

Combine all terms containing x.

$$\left(a-y\right)x=0$$

Divide 0 by a-y.

$$x=0$$

Variable x cannot be equal to 0.

$$x\in \emptyset$$