Solve 1/x+4/y=1/15

$$\frac { 1 } { x } + \frac { 4 } { y } = \frac { 1 } { 15 }$$

Solve for x

$$x=-\frac{15y}{60-y}$$

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

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 15xy, the least common multiple of x,y,15.

$$15y+15x\times 4=xy$$

Multiply 15 and 4 to get 60.

$$15y+60x=xy$$

Subtract xy from both sides.

$$15y+60x-xy=0$$

Subtract 15y from both sides. Anything subtracted from zero gives its negation.

$$60x-xy=-15y$$

Combine all terms containing x.

$$\left(60-y\right)x=-15y$$

Divide both sides by 60-y.

$$\frac{\left(60-y\right)x}{60-y}=-\frac{15y}{60-y}$$

Dividing by 60-y undoes the multiplication by 60-y.

$$x=-\frac{15y}{60-y}$$

Variable x cannot be equal to 0.

$$x=-\frac{15y}{60-y}\text{, }x\neq 0$$

Solve for y

$$y=-\frac{60x}{15-x}$$

$$x\neq 0\text{ and }x\neq 15$$

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 15xy, the least common multiple of x,y,15.

$$15y+15x\times 4=xy$$

Multiply 15 and 4 to get 60.

$$15y+60x=xy$$

Subtract xy from both sides.

$$15y+60x-xy=0$$

Subtract 60x from both sides. Anything subtracted from zero gives its negation.

$$15y-xy=-60x$$

Combine all terms containing y.

$$\left(15-x\right)y=-60x$$

Divide both sides by 15-x.

$$\frac{\left(15-x\right)y}{15-x}=-\frac{60x}{15-x}$$

Dividing by 15-x undoes the multiplication by 15-x.

$$y=-\frac{60x}{15-x}$$

Variable y cannot be equal to 0.

$$y=-\frac{60x}{15-x}\text{, }y\neq 0$$