Rational expressions

Question

Simplify the expression.

Indentify the restriction on the domain.

 6x^2 + x - 12   divided by  3x^2 + 14x - 24

Answer 1

6x²+x-12=(3x-4)(2x+3); 3x²+14x-24=(3x-4)(x+6).

(6x²+x-12)/(3x²+14x-24)=(2x+3)/(x+6) provided 3x-4≠0, that is, x≠4/3 (x=4/3 leads to a hole).

Also x+6≠0, that is, x≠-6 (x=6 leads to an asymptote).

So the restrictions on the domain is that x is neither 4/3 or -6.