Solve x+4/x=z/z+4

$$\frac { x + 4 } { x } = \frac { z } { z + 4 }$$

Solve for x

$$x=-\left(z+4\right)$$

$$z\neq -4$$

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(z+4\right), the least common multiple of x,z+4.

$$\left(z+4\right)\left(x+4\right)=xz$$

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

$$zx+4z+4x+16=xz$$

Subtract xz from both sides.

$$zx+4z+4x+16-xz=0$$

Combine zx and -xz to get 0.

$$4z+4x+16=0$$

Subtract 4z from both sides. Anything subtracted from zero gives its negation.

$$4x+16=-4z$$

Subtract 16 from both sides.

$$4x=-4z-16$$

Divide both sides by 4.

$$\frac{4x}{4}=\frac{-4z-16}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$x=\frac{-4z-16}{4}$$

Divide -4z-16 by 4.

$$x=-z-4$$

Variable x cannot be equal to 0.

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

Solve for z

$$z=-\left(x+4\right)$$

$$x\neq 0$$

Steps for Solving Linear Equation

Variable z cannot be equal to -4 since division by zero is not defined. Multiply both sides of the equation by x\left(z+4\right), the least common multiple of x,z+4.

$$\left(z+4\right)\left(x+4\right)=xz$$

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

$$zx+4z+4x+16=xz$$

Subtract xz from both sides.

$$zx+4z+4x+16-xz=0$$

Combine zx and -xz to get 0.

$$4z+4x+16=0$$

Subtract 4x from both sides. Anything subtracted from zero gives its negation.

$$4z+16=-4x$$

Subtract 16 from both sides.

$$4z=-4x-16$$

Divide both sides by 4.

$$\frac{4z}{4}=\frac{-4x-16}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$z=\frac{-4x-16}{4}$$

Divide -4x-16 by 4.

$$z=-x-4$$

Variable z cannot be equal to -4.

$$z=-x-4\text{, }z\neq -4$$