Solve 4/x-4/y=4

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

Solve for x

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

$$y\neq 0\text{ and }y\neq -1$$

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.

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

Subtract 4xy from both sides.

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

Subtract y\times 4 from both sides. Anything subtracted from zero gives its negation.

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

Multiply -1 and 4 to get -4.

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

Multiply -1 and 4 to get -4.

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

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by -4-4y.

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

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

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

Divide -4y by -4-4y.

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

Variable x cannot be equal to 0.

$$x=\frac{y}{y+1}\text{, }x\neq 0$$

Solve for y

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

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

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.

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

Subtract 4xy from both sides.

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

Add x\times 4 to both sides. Anything plus zero gives itself.

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

Combine all terms containing y.

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

The equation is in standard form.

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

Divide both sides by 4-4x.

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

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

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

Divide 4x by 4-4x.

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

Variable y cannot be equal to 0.

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