Question

Part b) Rewrite each expression as an equivalent rational expression using the LCD:

Answer 1

The Solution:

Given these expressions:

$\begin{gathered} \frac{4}{p^2+7p+12} \\ \\ \\ \frac{3p}{p^2+8p+15} \end{gathered}$

We are asked to use the Lowest Common Denominator to rewrite each expression as an equivalent rational expression.

Step 1:

Use the Factor Method of solving a quadratic expression to resolve each of the denominators.

$\frac{4}{p^{2}+7p+12}=\frac{4}{p^2+3p+4p+12}=\frac{4}{p(p+3)+4(p+3)}=\frac{4}{(p+3)(p+4)}$

Step 2:

Similarly,

$\frac{3p}{p^{2}+8p+15}=\frac{3p}{p^2+3p+5p+15}=\frac{3p}{p(p+3)+5(p+3)}=\frac{3p}{(p+3)(p+5)}$

Therefore, the correct answers are respectively:

$\begin{gathered} \frac{4}{p^2+7p+12}=\frac{4}{(p+3)(p+4)} \\ \\ \frac{3p}{p^{2}+8p+15}=\frac{3p}{(p+3)(p+5)} \end{gathered}$