Question

What is the relationship between a and b

Answer 1

Since $x^2-4$ is continuous at x=3 (basically no interruption of any form), we can do direct substitution and plug in x=3.

$6 = \displaystyle\lim_{x\to3} f(x) = f(3) = \dfrac{a(3)^2-b}{(3)^2-4} = \dfrac{9a-b}{5}$

So then the relationship between a and b would be $\boxed{9a-b = 30}$

Hope this helps.