Solve 1/x+1/y=5/40

$$\frac { 1 } { x } + \frac { 1 } { y } = \frac { 5 } { 40 }$$

Solve for x

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

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

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 40xy, the least common multiple of x,y,40.

$$40y+40x=xy\times 5$$

Subtract xy\times 5 from both sides.

$$40y+40x-xy\times 5=0$$

Multiply -1 and 5 to get -5.

$$40y+40x-5xy=0$$

Subtract 40y from both sides. Anything subtracted from zero gives its negation.

$$40x-5xy=-40y$$

Combine all terms containing x.

$$\left(40-5y\right)x=-40y$$

Divide both sides by 40-5y.

$$\frac{\left(40-5y\right)x}{40-5y}=-\frac{40y}{40-5y}$$

Dividing by 40-5y undoes the multiplication by 40-5y.

$$x=-\frac{40y}{40-5y}$$

Divide -40y by 40-5y.

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

Variable x cannot be equal to 0.

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

Solve for y

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

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

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 40xy, the least common multiple of x,y,40.

$$40y+40x=xy\times 5$$

Subtract xy\times 5 from both sides.

$$40y+40x-xy\times 5=0$$

Multiply -1 and 5 to get -5.

$$40y+40x-5xy=0$$

Subtract 40x from both sides. Anything subtracted from zero gives its negation.

$$40y-5xy=-40x$$

Combine all terms containing y.

$$\left(40-5x\right)y=-40x$$

Divide both sides by 40-5x.

$$\frac{\left(40-5x\right)y}{40-5x}=-\frac{40x}{40-5x}$$

Dividing by 40-5x undoes the multiplication by 40-5x.

$$y=-\frac{40x}{40-5x}$$

Divide -40x by 40-5x.

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

Variable y cannot be equal to 0.

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