Question

Simplify$\frac{{\mathrm{x}}^2+7\mathrm{x}+12}{{\mathrm{x}}^2+8\mathrm{x}+16}$

Short answer

Final answer is$\frac{(\mathrm{x}+3)}{(\mathrm{x}+4)}.$

Step-by-step solution

Step 1. Given Data

Given that the expression is$\frac{{\mathrm{x}}^2+7\mathrm{x}+12}{{\mathrm{x}}^2+8\mathrm{x}+16}.$

Step 2. Simplification

On simplifying numerator and denominator using AC factorization,

$$\begin{gathered} =\frac{{\mathrm{x}}^2+4\mathrm{x}+3\mathrm{x}+12}{{\mathrm{x}}^2+4\mathrm{x}+4\mathrm{x}+16} \\ =\frac{\mathrm{x}(\mathrm{x}+4)+3(\mathrm{x}+4)}{\mathrm{x}(\mathrm{x}+4)+4(\mathrm{x}+4)} \\ =\frac{(\mathrm{x}+4)(\mathrm{x}+3)}{(\mathrm{x}+4)(\mathrm{x}+4)} \end{gathered}$$

On dividing the common factor,

$=\frac{(\mathrm{x}+3)}{(\mathrm{x}+4)}$