Solve z/x-5/x-3=0

$$\frac { z } { x } - \frac { 5 } { x - 3 } = 0$$

Solve for x

$$x=\frac{3z}{z-5}$$

$$z\neq 0\text{ and }z\neq 5$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 0,3 since division by zero is not defined. Multiply both sides of the equation by x\left(x-3\right), the least common multiple of x,x-3.

$$\left(x-3\right)z-x\times 5=0$$

Use the distributive property to multiply x-3 by z.

$$xz-3z-x\times 5=0$$

Add 3z to both sides. Anything plus zero gives itself.

$$xz-x\times 5=3z$$

Multiply -1 and 5 to get -5.

$$xz-5x=3z$$

Combine all terms containing x.

$$\left(z-5\right)x=3z$$

Divide both sides by z-5.

$$\frac{\left(z-5\right)x}{z-5}=\frac{3z}{z-5}$$

Dividing by z-5 undoes the multiplication by z-5.

$$x=\frac{3z}{z-5}$$

Variable x cannot be equal to any of the values 3,0.

$$x=\frac{3z}{z-5}\text{, }x\neq 3\text{ and }x\neq 0$$

Solve for z

$$z=\frac{5x}{x-3}$$

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

Steps for Solving Linear Equation

Multiply both sides of the equation by x\left(x-3\right), the least common multiple of x,x-3.

$$\left(x-3\right)z-x\times 5=0$$

Use the distributive property to multiply x-3 by z.

$$xz-3z-x\times 5=0$$

Add x\times 5 to both sides. Anything plus zero gives itself.

$$xz-3z=x\times 5$$

Combine all terms containing z.

$$\left(x-3\right)z=x\times 5$$

The equation is in standard form.

$$\left(x-3\right)z=5x$$

Divide both sides by x-3.

$$\frac{\left(x-3\right)z}{x-3}=\frac{5x}{x-3}$$

Dividing by x-3 undoes the multiplication by x-3.

$$z=\frac{5x}{x-3}$$