Simplify completely quantity 12 x plus 36 over quantity x squared minus 4 x minus 21 and find the restrictions on the variable ...

To simplify the expression stated, it is better to write it in the numerical form. The statement is:

quantity 12 x plus 36 over quantity x squared minus 4 x minus 21

The numerical form is:

12x+36 / (x ²-4x-21)

Simplifying,

12x+36 / (x ²-4x-21)

12 (x+3) / (x+3) (x-7)

We can cancel the x+3 term, leaving only:

12 / (x - 7)

The answer is 12/x-7, x ≠ 7, x ≠ - 3