Solve y=2(x-a)/x

$$y = \frac { 2 ( x - a ) } { x }$$

Solve for a

$$a=-\frac{xy}{2}+x$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x.

$$yx=2\left(x-a\right)$$

Use the distributive property to multiply 2 by x-a.

$$yx=2x-2a$$

Swap sides so that all variable terms are on the left hand side.

$$2x-2a=yx$$

Subtract 2x from both sides.

$$-2a=yx-2x$$

The equation is in standard form.

$$-2a=xy-2x$$

Divide both sides by -2.

$$\frac{-2a}{-2}=\frac{x\left(y-2\right)}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$a=\frac{x\left(y-2\right)}{-2}$$

Divide x\left(-2+y\right) by -2.

$$a=-\frac{xy}{2}+x$$

Solve for x

$$\left\{\begin{matrix}x=\frac{2a}{2-y}\text{, }&a\neq 0\text{ and }y\neq 2\\x\neq 0\text{, }&a=0\text{ and }y=2\end{matrix}\right.$$

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.

$$yx=2\left(x-a\right)$$

Use the distributive property to multiply 2 by x-a.

$$yx=2x-2a$$

Subtract 2x from both sides.

$$yx-2x=-2a$$

Combine all terms containing x.

$$\left(y-2\right)x=-2a$$

Divide both sides by y-2.

$$\frac{\left(y-2\right)x}{y-2}=-\frac{2a}{y-2}$$

Dividing by y-2 undoes the multiplication by y-2.

$$x=-\frac{2a}{y-2}$$

Variable x cannot be equal to 0.

$$x=-\frac{2a}{y-2}\text{, }x\neq 0$$