Solve z+4/z=sqrt{3}

$$\frac{ z+4 }{ z } = \sqrt{ 3 }$$

Solve for z

$$z=2\left(\sqrt{3}+1\right)\approx 5.464101615$$

Steps for Solving Linear Equation

Variable z cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by z.

$$z+4=z\sqrt{3}$$

Subtract z\sqrt{3} from both sides.

$$z+4-z\sqrt{3}=0$$

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

$$z-z\sqrt{3}=-4$$

Combine all terms containing z.

$$\left(1-\sqrt{3}\right)z=-4$$

Divide both sides by 1-\sqrt{3}.

$$\frac{\left(1-\sqrt{3}\right)z}{1-\sqrt{3}}=-\frac{4}{1-\sqrt{3}}$$

Dividing by 1-\sqrt{3} undoes the multiplication by 1-\sqrt{3}.

$$z=-\frac{4}{1-\sqrt{3}}$$

Divide -4 by 1-\sqrt{3}.

$$z=2\sqrt{3}+2$$