Answer: x+2 / x+ 9, x = -2, x=-9 ( A )
Solution:
Breakdown the problem into two sets
Step 1: simplify x^2 -10x - 24
Factorize the above equation,
Multiply the last term (24) with the first term coefficient i.e. 1
Step 2: Then, find the factors of 24 in a way that when you add or subtract it sums up to 10
x2 - 12x + 2x - 24 >>>> (x2-12x) + (2x-24) >>> take common
>>>> x(x-12) + 2( x-12)
Step 3: (x + 2) (x - 12)
Step 4: Step 1: simplify x^2 - 3x - 108 using the same steps
x2 - 12x + 9x - 108 >>>> take common x(x-12) + 9 ( x -12) >>>
(x + 9) (x - 12) final product
Now, Simplify the equation as a whole
(x + 2) (x - 12) / (x + 9) (x - 12) Note: (x - 12) cancels out
= (x + 2) / (x + 9) with x= -2 and x= -9
