Hello! Here is your answer for this question!
Answer: 12 / x-7
Restrictions on the variable are... x ≠ 7, x ≠ -3
Step-by-step explanation: Factor the denominator and cancel the common factors where possible.
12x+36 / x^2 - 4x - 21
The numerator will and can be factored...
12x+36=12(x+3)
The denominator x^2-4x-21 has a discriminant.
D=(-4)^2-4•(-21)•1=16+84=100
Then... x1,2 = -(-4)±√100 / 2•1 = 4±10 / 2 = 7, -3
Then (once more)... x^2-4x-21=(x-7)(x+3)
So, this give you your restrictions, x ≠ 7, x ≠ -3
Simplify fraction...
12x+36 / x^2-4x-21 = 12(x+3) / (x-7)(x+3) = 12 / x-7
Hope this helps you out! ☺