Solve 1/x+1/y=19/94

$$\frac { 1 } { x } + \frac { 1 } { y } = \frac { 19 } { 94 }$$

Solve for x

$$x=-\frac{94y}{94-19y}$$

$$y\neq 0\text{ and }y\neq \frac{94}{19}$$

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 94xy, the least common multiple of x,y,94.

$$94y+94x=19xy$$

Subtract 19xy from both sides.

$$94y+94x-19xy=0$$

Subtract 94y from both sides. Anything subtracted from zero gives its negation.

$$94x-19xy=-94y$$

Combine all terms containing x.

$$\left(94-19y\right)x=-94y$$

Divide both sides by 94-19y.

$$\frac{\left(94-19y\right)x}{94-19y}=-\frac{94y}{94-19y}$$

Dividing by 94-19y undoes the multiplication by 94-19y.

$$x=-\frac{94y}{94-19y}$$

Variable x cannot be equal to 0.

$$x=-\frac{94y}{94-19y}\text{, }x\neq 0$$

Solve for y

$$y=-\frac{94x}{94-19x}$$

$$x\neq 0\text{ and }x\neq \frac{94}{19}$$

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 94xy, the least common multiple of x,y,94.

$$94y+94x=19xy$$

Subtract 19xy from both sides.

$$94y+94x-19xy=0$$

Subtract 94x from both sides. Anything subtracted from zero gives its negation.

$$94y-19xy=-94x$$

Combine all terms containing y.

$$\left(94-19x\right)y=-94x$$

Divide both sides by 94-19x.

$$\frac{\left(94-19x\right)y}{94-19x}=-\frac{94x}{94-19x}$$

Dividing by 94-19x undoes the multiplication by 94-19x.

$$y=-\frac{94x}{94-19x}$$

Variable y cannot be equal to 0.

$$y=-\frac{94x}{94-19x}\text{, }y\neq 0$$