Solve y=x/a*1-x/x

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

Solve for x

$$x\neq 0$$

$$y=-1+\frac{1}{a}\text{ and }a\neq 0$$

Steps for Solving Linear Equation

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

$$yx=\frac{x}{a\times 1}-x$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{a\times 1}{a\times 1}.

$$yx=\frac{x}{a\times 1}-\frac{xa\times 1}{a\times 1}$$

Since \frac{x}{a\times 1} and \frac{xa}{a} have the same denominator, subtract them by subtracting their numerators.

$$yx=\frac{x-xa}{a\times 1}$$

Subtract \frac{x-xa}{a\times 1} from both sides.

$$yx-\frac{x-xa}{a\times 1}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply yx times \frac{a\times 1}{a\times 1}.

$$\frac{yxa\times 1}{a\times 1}-\frac{x-xa}{a\times 1}=0$$

Since \frac{yxa\times 1}{a\times 1} and \frac{x-xa}{a} have the same denominator, subtract them by subtracting their numerators.

$$\frac{yxa\times 1-\left(x-xa\right)}{a\times 1}=0$$

Do the multiplications in yxa\times 1-\left(x-xa\right).

$$\frac{yxa-x+xa}{a\times 1}=0$$

Multiply both sides of the equation by a.

$$yxa-x+xa=0$$

Combine all terms containing x.

$$\left(ya-1+a\right)x=0$$

The equation is in standard form.

$$\left(ay+a-1\right)x=0$$

Divide 0 by ya-1+a.

$$x=0$$

Variable x cannot be equal to 0.

$$x\in \emptyset$$

Solve for a

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

$$y\neq -1\text{ and }x\neq 0$$