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 : )

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

step-by-step explanation:

1. practice, practice & more practice

2. review errors

3. master the key concepts

do not try to memorise the processes.

4. understand your doubts.

5. create a distraction free study environment

6. create a mathematical dictionary

7. apply maths to real world problems.

step-by-step explanation: