Solve 1/x+1/y=1/4

$$\frac { 1 } { x } + \frac { 1 } { y } = \frac { 1 } { 4 }$$

Solve for x

$$x=-\frac{4y}{4-y}$$

$$y\neq 0\text{ and }y\neq 4$$

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 4xy, the least common multiple of x,y,4.

$$4y+4x=xy$$

Subtract xy from both sides.

$$4y+4x-xy=0$$

Subtract 4y from both sides. Anything subtracted from zero gives its negation.

$$4x-xy=-4y$$

Combine all terms containing x.

$$\left(4-y\right)x=-4y$$

Divide both sides by 4-y.

$$\frac{\left(4-y\right)x}{4-y}=-\frac{4y}{4-y}$$

Dividing by 4-y undoes the multiplication by 4-y.

$$x=-\frac{4y}{4-y}$$

Variable x cannot be equal to 0.

$$x=-\frac{4y}{4-y}\text{, }x\neq 0$$

Solve for y

$$y=-\frac{4x}{4-x}$$

$$x\neq 0\text{ and }x\neq 4$$

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 4xy, the least common multiple of x,y,4.

$$4y+4x=xy$$

Subtract xy from both sides.

$$4y+4x-xy=0$$

Subtract 4x from both sides. Anything subtracted from zero gives its negation.

$$4y-xy=-4x$$

Combine all terms containing y.

$$\left(4-x\right)y=-4x$$

Divide both sides by 4-x.

$$\frac{\left(4-x\right)y}{4-x}=-\frac{4x}{4-x}$$

Dividing by 4-x undoes the multiplication by 4-x.

$$y=-\frac{4x}{4-x}$$

Variable y cannot be equal to 0.

$$y=-\frac{4x}{4-x}\text{, }y\neq 0$$