Question

Simplify completely

x^2 -10x - 24 / x^2 - 3x - 108

A) x+2 / x+ 9, x = -2, x=-9
B) x+2 / x+ 9, x= -9, x= 12
C) x-2 / x- 9, x= -2, x= -9
D) x-2 / x -9, x= -9, x= 12

ASAP PLEASE!! :)

Answer 1

x+2/x+9, x= -9, x=12

Answer 2

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