Question

x^2 + 5x +6/
x^2 - 3x -10

How do I do this? Is it asking me to divide?
The answer choices are as following:

A)x + 3/
x - 5

, x ≠ 5


B)x + 3/
x - 5

, x ≠ -2, 5


C)x2 + 5x + 6/
x - 5

, x ≠ 5


D)x2 + 5x + 6/
x - 5

, x ≠ -2, 5

Answer 1

I suppose the question is to simplify the expression:
(x^2 + 5x +6) / (x^2 - 3x -10)

The numerator and denominator can be factorized and rewritten as:

((x+2)(x+3)) / ((x+2)(x-5))

If x≠-1, then can can cancel the common factor (x+2) and reduce the expression to:
(x+3)/(x-5)
The expression exists if x≠5.

Thus the answer for the simplified expression is
(x+3)/(x-5) where x≠-2,5