Question

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

Answer 1

\[\frac{ 12x + 36 }{ x^2 -4x -21 }\] We want to factor the top and bottom. From the top, we can pull out a 12, because it's in each term. On the bottom, we can factor. We're looking for two factors that multiply to -21 and add to -4, which would be -7 and +3:
\[\frac{ 12(x+3) }{ (x-7)(x+3) }\] Do you see what we could do from here?