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

Question

asked Jul 6, 2020 129k views

2 Answers

Johnny Bones · Answer 1 · 2020-07-11T05:22:24+0000

Answer:

The correct answer is option B.

Explanation:

The given rational expression is:

(x^2-4)/(x^2+5x+6)

Factor the numerator and the denominator:

(x^2-2^2)/(x^2+2x+3x+6)

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

((x-2))/(x(x+2)+3(x+2))

((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:

(x-2)/(x+3)

The correct choice is the second option.