Answer: (x + 3) / (x - 2)(x - 3)(x - 4)
Step-by-step explanation:
The problem given can be viewed as
a/b over c/d
where a/b is the top fraction and c/d is the bottom fraction.
This can be rearranged to
a × d / b × c
So, you will have:
(x + 4)(x + 3) / (x² - 5x + 6)(x² - 16)
Now, factor the two bottom polynomials so you end up with:
(x + 4)(x + 3) / (x - 2)(x - 3)(x + 4)(x - 4)
Cancel the (x + 4) on the top and bottom so you’re left with the answer:
(x + 3) / (x - 2)(x - 3)(x - 4)
If you need to find the solutions to x, set the denominator equal to zero.
x = 2
x = 3
x = 4
