Solve 1/x-3/y=4

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

Solve for x

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

$$y\neq 0\text{ and }y\neq -\frac{3}{4}$$

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 x,y.

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

Subtract 4xy from both sides.

$$y-x\times 3-4xy=0$$

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

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

Multiply -1 and 3 to get -3.

$$-3x-4xy=-y$$

Combine all terms containing x.

$$\left(-3-4y\right)x=-y$$

The equation is in standard form.

$$\left(-4y-3\right)x=-y$$

Divide both sides by -3-4y.

$$\frac{\left(-4y-3\right)x}{-4y-3}=-\frac{y}{-4y-3}$$

Dividing by -3-4y undoes the multiplication by -3-4y.

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

Divide -y by -3-4y.

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

Variable x cannot be equal to 0.

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

Solve for y

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

$$x\neq 0\text{ and }x\neq \frac{1}{4}$$

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 x,y.

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

Subtract 4xy from both sides.

$$y-x\times 3-4xy=0$$

Add x\times 3 to both sides. Anything plus zero gives itself.

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

Combine all terms containing y.

$$\left(1-4x\right)y=x\times 3$$

The equation is in standard form.

$$\left(1-4x\right)y=3x$$

Divide both sides by 1-4x.

$$\frac{\left(1-4x\right)y}{1-4x}=\frac{3x}{1-4x}$$

Dividing by 1-4x undoes the multiplication by 1-4x.

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

Variable y cannot be equal to 0.

$$y=\frac{3x}{1-4x}\text{, }y\neq 0$$