Question

Simplify the rational expression x^2-4/x^2+5x+6. State any restrictions on the variable.

Answer 1

Answer:

The correct answer is option B.

Step-by-step explanation:

The given rational expression is:

$\frac{x^2-4}{x^2+5x+6}$

Factor the numerator and the denominator:

$\frac{x^2-2^2}{x^2+2x+3x+6}$

Factor the numerator using difference of two squares and the denominator using factorization by grouping.

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

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

This function is defined if and only if the denominator is not zero.

That is: (x+3)(x+2)≠0.

x≠-2,x≠-3

We simplify now to obtain:

$\frac{x-2}{x+3}$

The correct choice is the second option.