Solve 1/x+1/y=3/2=

$$\frac{ 1 }{ x } + \frac{ 1 }{ y } = \frac{ 3 }{ 2 } =$$

Solve for x

$$x=-\frac{2y}{2-3y}$$

$$y\neq 0\text{ and }y\neq \frac{2}{3}$$

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 2xy, the least common multiple of x,y,2.

$$2y+2x=3xy$$

Subtract 3xy from both sides.

$$2y+2x-3xy=0$$

Subtract 2y from both sides. Anything subtracted from zero gives its negation.

$$2x-3xy=-2y$$

Combine all terms containing x.

$$\left(2-3y\right)x=-2y$$

Divide both sides by 2-3y.

$$\frac{\left(2-3y\right)x}{2-3y}=-\frac{2y}{2-3y}$$

Dividing by 2-3y undoes the multiplication by 2-3y.

$$x=-\frac{2y}{2-3y}$$

Variable x cannot be equal to 0.

$$x=-\frac{2y}{2-3y}\text{, }x\neq 0$$

Solve for y

$$y=-\frac{2x}{2-3x}$$

$$x\neq 0\text{ and }x\neq \frac{2}{3}$$

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 2xy, the least common multiple of x,y,2.

$$2y+2x=3xy$$

Subtract 3xy from both sides.

$$2y+2x-3xy=0$$

Subtract 2x from both sides. Anything subtracted from zero gives its negation.

$$2y-3xy=-2x$$

Combine all terms containing y.

$$\left(2-3x\right)y=-2x$$

Divide both sides by 2-3x.

$$\frac{\left(2-3x\right)y}{2-3x}=-\frac{2x}{2-3x}$$

Dividing by 2-3x undoes the multiplication by 2-3x.

$$y=-\frac{2x}{2-3x}$$

Variable y cannot be equal to 0.

$$y=-\frac{2x}{2-3x}\text{, }y\neq 0$$