Solve 4/x=y+4/y-8

$$\frac { 4 } { x } = \frac { y + 4 } { y - 8 }$$

Solve for x

$$x=\frac{4\left(y-8\right)}{y+4}$$

$$y\neq 8\text{ and }y\neq -4$$

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 x\left(y-8\right), the least common multiple of x,y-8.

$$\left(y-8\right)\times 4=x\left(y+4\right)$$

Use the distributive property to multiply y-8 by 4.

$$4y-32=x\left(y+4\right)$$

Use the distributive property to multiply x by y+4.

$$4y-32=xy+4x$$

Swap sides so that all variable terms are on the left hand side.

$$xy+4x=4y-32$$

Combine all terms containing x.

$$\left(y+4\right)x=4y-32$$

Divide both sides by y+4.

$$\frac{\left(y+4\right)x}{y+4}=\frac{4y-32}{y+4}$$

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

$$x=\frac{4y-32}{y+4}$$

Divide -32+4y by y+4.

$$x=\frac{4\left(y-8\right)}{y+4}$$

Variable x cannot be equal to 0.

$$x=\frac{4\left(y-8\right)}{y+4}\text{, }x\neq 0$$

Solve for y

$$y=\frac{4\left(x+8\right)}{4-x}$$

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

Steps for Solving Linear Equation

Variable y cannot be equal to 8 since division by zero is not defined. Multiply both sides of the equation by x\left(y-8\right), the least common multiple of x,y-8.

$$\left(y-8\right)\times 4=x\left(y+4\right)$$

Use the distributive property to multiply y-8 by 4.

$$4y-32=x\left(y+4\right)$$

Use the distributive property to multiply x by y+4.

$$4y-32=xy+4x$$

Subtract xy from both sides.

$$4y-32-xy=4x$$

Add 32 to both sides.

$$4y-xy=4x+32$$

Combine all terms containing y.

$$\left(4-x\right)y=4x+32$$

Divide both sides by 4-x.

$$\frac{\left(4-x\right)y}{4-x}=\frac{4x+32}{4-x}$$

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

$$y=\frac{4x+32}{4-x}$$

Divide 32+4x by 4-x.

$$y=\frac{4\left(x+8\right)}{4-x}$$

Variable y cannot be equal to 8.

$$y=\frac{4\left(x+8\right)}{4-x}\text{, }y\neq 8$$