Question

In the following exercises, simplify.

$\frac{2+{\displaystyle \frac{1}{p-3}}}{{\displaystyle \frac{5}{p-3}}}$

Short answer

The simplified expression is$\frac{2p-5}{5}$

Step-by-step solution

Step 1. Given information

The given Expression is

$\frac{2+{\displaystyle \frac{1}{p-3}}}{{\displaystyle \frac{5}{p-3}}}$

Step 2. Simplify the expression

$$\begin{gathered} \frac{2+{\displaystyle \frac{1}{p-3}}}{{\displaystyle \frac{5}{p-3}}}=\frac{\left(\cancel{p-3}\right)\left(2+{\displaystyle \frac{1}{\left(\cancel{p-3}\right)}}\right)}{\left(\cancel{p-3}\right)\left({\displaystyle \frac{5}{\left(\cancel{p-3}\right)}}\right)} \\ =\frac{2\left(p-3\right)+1}{5} \\ =\frac{2p-5}{5} \end{gathered}$$

The simplified expression is$\frac{2p-5}{5}$

Step 3. The solution

The simplified expression is$\frac{2p-5}{5}$