Question

Simplify the rational expression$\frac{p^3+3p^2+4p+12}{p^2+p-6}.$

Short answer

Simplified form of the given rational expression $\frac{p^3+3p^2+4p+12}{p^2+p-6}is\frac{p^2+4}{p-2};p\ne 2$$\frac{p^3+3p^2+4p+12}{p^2+p-6}is\frac{(p^2+4)}{(p-2)}.$

Step-by-step solution

Step 1.  Given information

Given rational expression is $\frac{p^3+3p^2+4p+12}{p^2+p-6}.$

We have to simplify the the given expression.

Step 2. Simplification of the rational expression

For simplification factor, the numerator and denominator separately, find the common factor and then simplify.

Hence simplified form is $$\begin{gathered} \frac{p^3+3p^2+4p+12}{p^2+p-6}=\frac{p^2(p+3)+4(p+3)}{(p+3)(p-2)} \\ =\frac{(p+3)(p^2+4)}{(p+3)(p-2)} \\ =\frac{p^2+4}{P-2};p\ne 2 \end{gathered}$$