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

factor it
( x^2 + 5x +6)/( x^2 - 3x -10)
= (x+2)(x+3)/[(x-5)(x+2)]
= (x+3)/(x-5) , x ≠ -2,5


suppose you had (2)(3)/[(3)(7)]
could you not cancel the equal factors to get 2/7
the above question follows the same concept, I canceled the factors (x+2).

Answer 2

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

factor top and bottom
(x+2)(x+3) / [(x-5)(x+2]

= (x+3) / (x-5)
if x = 5 denominator is zero so exclude that point from the domain of x so I say A