Question

Consider the functions f(x)=(ax^2-b)/(x^2-4) and g(x)=(x^2-cx+d). if the limit as x approaches 3 equals 6, what is the relationship between a and b?

Answer 1

$6=\dfrac{a\cdot3^2-b}{3^2-4}\\\\ 6=\dfrac{9a-b}{5}\\\\\ 9a-b=30\\\\ \boxed{b=9a-30}$