Question

The lowest form of the algebraic expression $\frac{a^2+5a+6}{a^2-a-6}$ is

• A. $\frac{a+3}{a-3}$
• B. $\frac{a-3}{a-3}$
• C. $a+3$
• D. $\frac{a+3}{a+3}$

Answer 1

The correct option is A $\frac{a+3}{a-3}$

$\frac{a^2+5a+6}{a^2-a-6}$
Factor of $a^2+5a+6=(a+3)(a+2)$
$\therefore a^2-a-6=(a-3)(a+2)$
So, $\frac{a^2+5a+6}{a^2-a-6}=\frac{(a+3)(a+2)}{(a-3)(a+2)}$
$=$ $\frac{a+3}{a-3}$