Solve z/x=0/x+5

$$\frac { z } { x } = \frac { 0 } { x + 5 }$$

Solve for x (complex solution)

$$x\in \mathrm{C}\setminus 0,-5$$

$$z=0$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -5,0 since division by zero is not defined. Multiply both sides of the equation by x\left(x+5\right), the least common multiple of x,x+5.

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

Use the distributive property to multiply x+5 by z.

$$xz+5z=x\times 0$$

Anything times zero gives zero.

$$xz+5z=0$$

Subtract 5z from both sides. Anything subtracted from zero gives its negation.

$$xz=-5z$$

The equation is in standard form.

$$zx=-5z$$

Divide both sides by z.

$$\frac{zx}{z}=-\frac{5z}{z}$$

Dividing by z undoes the multiplication by z.

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

Divide -5z by z.

$$x=-5$$

Variable x cannot be equal to -5.

$$x\in \emptyset$$

Solve for x

$$x\in \mathrm{R}\setminus 0,-5$$

$$z=0$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -5,0 since division by zero is not defined. Multiply both sides of the equation by x\left(x+5\right), the least common multiple of x,x+5.

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

Use the distributive property to multiply x+5 by z.

$$xz+5z=x\times 0$$

Anything times zero gives zero.

$$xz+5z=0$$

Subtract 5z from both sides. Anything subtracted from zero gives its negation.

$$xz=-5z$$

The equation is in standard form.

$$zx=-5z$$

Divide both sides by z.

$$\frac{zx}{z}=-\frac{5z}{z}$$

Dividing by z undoes the multiplication by z.

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

Divide -5z by z.

$$x=-5$$

Variable x cannot be equal to -5.

$$x\in \emptyset$$

Solve for z

$$z=0$$

$$x\neq 0\text{ and }x\neq -5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x\left(x+5\right), the least common multiple of x,x+5.

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

Use the distributive property to multiply x+5 by z.

$$xz+5z=x\times 0$$

Anything times zero gives zero.

$$xz+5z=0$$

Combine all terms containing z.

$$\left(x+5\right)z=0$$

Divide 0 by x+5.

$$z=0$$