Simplify completely quantity 12 x plus 36 over quantity x squared minus 4 x minus 21 and find the restrictions on the variable.
12 over quantity x minus 7, x ≠ 7
12 over quantity x minus 7, x ≠ 7, x ≠ −3
quantity x plus 3 over quantity x minus 7, x ≠ 7
quantity x plus 3 over quantity x minus 7, x ≠ 7, x ≠ −3

ANSWER



EXPLANATION

We want to simplify

,

This Rational function is defined, for

,





In order to simplify the above rational function, we need to factor both the numerator and the denominator.

Let us factor the numerator first to get,



As for the denominator, we need to split the middle term of the quadratic trinomial to get,



We factor to obtain,



We factor further to obtain,



We cancel out common factors to get,



where

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