Question

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

Answer 1

Option B is correct.

I just took the semester review.

Answer 2

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.