Simplify completly 12x+36 over x^2-4x-21 and find the restrictions on the variable

Hello! Here is your answer for this question!

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! ☺

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