Solve 1/x+1/y=5/8

$$\frac { 1 } { x } + \frac { 1 } { y } = \frac { 5 } { 8 }$$

Solve for x

$$x=-\frac{8y}{8-5y}$$

$$y\neq 0\text{ and }y\neq \frac{8}{5}$$

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 8xy, the least common multiple of x,y,8.

$$8y+8x=5xy$$

Subtract 5xy from both sides.

$$8y+8x-5xy=0$$

Subtract 8y from both sides. Anything subtracted from zero gives its negation.

$$8x-5xy=-8y$$

Combine all terms containing x.

$$\left(8-5y\right)x=-8y$$

Divide both sides by 8-5y.

$$\frac{\left(8-5y\right)x}{8-5y}=-\frac{8y}{8-5y}$$

Dividing by 8-5y undoes the multiplication by 8-5y.

$$x=-\frac{8y}{8-5y}$$

Variable x cannot be equal to 0.

$$x=-\frac{8y}{8-5y}\text{, }x\neq 0$$

Solve for y

$$y=-\frac{8x}{8-5x}$$

$$x\neq 0\text{ and }x\neq \frac{8}{5}$$

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 8xy, the least common multiple of x,y,8.

$$8y+8x=5xy$$

Subtract 5xy from both sides.

$$8y+8x-5xy=0$$

Subtract 8x from both sides. Anything subtracted from zero gives its negation.

$$8y-5xy=-8x$$

Combine all terms containing y.

$$\left(8-5x\right)y=-8x$$

Divide both sides by 8-5x.

$$\frac{\left(8-5x\right)y}{8-5x}=-\frac{8x}{8-5x}$$

Dividing by 8-5x undoes the multiplication by 8-5x.

$$y=-\frac{8x}{8-5x}$$

Variable y cannot be equal to 0.

$$y=-\frac{8x}{8-5x}\text{, }y\neq 0$$