Question

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

• A. $\frac{x-3}{x+3}$
• B. $\frac{x+3}{x-3}$
• C. $\frac{x+2}{x-3}$
• D. $\frac{x-3}{x+2}$

Answer 1

The correct option is B $\frac{x+3}{x-3}$

Let $A=x^2+5x+6$

$A=x^2+3x+2x+6$

$A=x(x+3)+2(x+3)$

$A=(x+2)(x+3)$

Let $B=x^2-x-6$

$B=x^2-3x+2x-6$

$B=x(x-3)+2(x-3)$

$B=(x-3)(x+2)$

$\frac{A}{B}=\frac{(x+2)(x+3)}{(x-3)(x+2)}=\frac{x+3}{x-3}$

$\therefore$ the lowest form of rational expression of $\frac{x^2+5x+6}{x^2-x+6}$ is $\frac{x+3}{x-3}$