Solve 4/y-1/x=3/xy

$$\frac{ 4 }{ y } - \frac{ 1 }{ x } = \frac{ 3 }{ xy }$$

Solve for x

$$x=\frac{y+3}{4}$$

$$y\neq -3\text{ and }y\neq 0$$

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

$$x\times 4-y=3$$

Add y to both sides.

$$x\times 4=3+y$$

The equation is in standard form.

$$4x=y+3$$

Divide both sides by 4.

$$\frac{4x}{4}=\frac{y+3}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$x=\frac{y+3}{4}$$

Variable x cannot be equal to 0.

$$x=\frac{y+3}{4}\text{, }x\neq 0$$

Solve for y

$$y=4x-3$$

$$x\neq \frac{3}{4}\text{ and }x\neq 0$$

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

$$x\times 4-y=3$$

Subtract x\times 4 from both sides.

$$-y=3-x\times 4$$

Multiply -1 and 4 to get -4.

$$-y=3-4x$$

Divide both sides by -1.

$$\frac{-y}{-1}=\frac{3-4x}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$y=\frac{3-4x}{-1}$$

Divide 3-4x by -1.

$$y=4x-3$$

Variable y cannot be equal to 0.

$$y=4x-3\text{, }y\neq 0$$