I've been out of the game for a long time so you can check my algebra to see that it's correct.
If , then
now take the limit as h goes to zero to find the equation for the slope of a tangent curve where the function f(x) is continuous ie. wherever x is not equal to 2. so, plug in x=3 after evaluating the limit
Of course, this is by using definition alone, but it's way easier if you prove the general case of curves of f(x) = g(x)/h(x) (which would give you quotient rule, which is a special case of product rule. essentially re-prove product rule if you haven't in class can save some time) and then use substitution of g(x) = x-1 and h(x) = x-2.