Solve 2/x-2/y=2/60

$$\frac { 2 } { x } - \frac { 2 } { y } = \frac { 2 } { 60 }$$

Solve for x

$$x=\frac{60y}{y+60}$$

$$y\neq 0\text{ and }y\neq -60$$

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 60xy, the least common multiple of x,y,60.

$$60y\times 2-60x\times 2=xy\times 2$$

Multiply 60 and 2 to get 120.

$$120y-60x\times 2=xy\times 2$$

Multiply 60 and 2 to get 120.

$$120y-120x=xy\times 2$$

Subtract xy\times 2 from both sides.

$$120y-120x-xy\times 2=0$$

Multiply -1 and 2 to get -2.

$$120y-120x-2xy=0$$

Subtract 120y from both sides. Anything subtracted from zero gives its negation.

$$-120x-2xy=-120y$$

Combine all terms containing x.

$$\left(-120-2y\right)x=-120y$$

The equation is in standard form.

$$\left(-2y-120\right)x=-120y$$

Divide both sides by -120-2y.

$$\frac{\left(-2y-120\right)x}{-2y-120}=-\frac{120y}{-2y-120}$$

Dividing by -120-2y undoes the multiplication by -120-2y.

$$x=-\frac{120y}{-2y-120}$$

Divide -120y by -120-2y.

$$x=\frac{60y}{y+60}$$

Variable x cannot be equal to 0.

$$x=\frac{60y}{y+60}\text{, }x\neq 0$$

Solve for y

$$y=-\frac{60x}{x-60}$$

$$x\neq 0\text{ and }x\neq 60$$

Steps for Solving Linear Equation

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 60xy, the least common multiple of x,y,60.

$$60y\times 2-60x\times 2=xy\times 2$$

Multiply 60 and 2 to get 120.

$$120y-60x\times 2=xy\times 2$$

Multiply 60 and 2 to get 120.

$$120y-120x=xy\times 2$$

Subtract xy\times 2 from both sides.

$$120y-120x-xy\times 2=0$$

Multiply -1 and 2 to get -2.

$$120y-120x-2xy=0$$

Add 120x to both sides. Anything plus zero gives itself.

$$120y-2xy=120x$$

Combine all terms containing y.

$$\left(120-2x\right)y=120x$$

Divide both sides by 120-2x.

$$\frac{\left(120-2x\right)y}{120-2x}=\frac{120x}{120-2x}$$

Dividing by 120-2x undoes the multiplication by 120-2x.

$$y=\frac{120x}{120-2x}$$

Divide 120x by 120-2x.

$$y=\frac{60x}{60-x}$$

Variable y cannot be equal to 0.

$$y=\frac{60x}{60-x}\text{, }y\neq 0$$