Question

In the following exercises, solve

$\frac{z}{16}+\frac{z+2}{4z}=\frac{1}{2z}$

Short answer

The solution is$z=0,-4.$

Step-by-step solution

Step 1. Given Information

The given rational expression is$\frac{z}{16}+\frac{z+2}{4z}=\frac{1}{2z}$

Step 2. Least Common Denominator(LCD)

The LCD is $16z$

Multiply the LCD on both sides,

$$\begin{gathered} \left(16z\right)\times [\frac{z}{16}+\frac{z+2}{4z}]=\frac{1}{2z}\times 16z \\ {z}^2+4(z+2)=8 \\ {z}^2+4z+8=8 \\ {z}^2+4z=0 \\ z(z+4)=0 \end{gathered}$$

Step 3. Solution of the equation

Using the zero product property,

$$\begin{gathered} z=0;z+4=0 \\ z=0;z=-4 \end{gathered}$$