If you look at your graph you see that there is a hole at x = 3. This results from a removeable discontinuity. That means that when we factor the numerator to (x-3)(x-1), that (x-3) cancels out between the numerator and denominator and a hole is what results from that cancelation. The other factor for the denominator is found where the vertical asymptote of the function is, which is found at x = -4. That means that the 2 factors for the denomonator are (x-3) and (x+4). When you FOIL those out, you get . That means that a = 1 and b = -12
To solve this problem you must apply the proccedure shown below:
1. You have that varies jointly as
and
and inversely as the product of
and
. Therefore, you can write the following equation, where
is the constant of proportionality:
2. Now, you must solve for the constant of proportionality, as following:
3. Susbtiute values:
4. Substitute the value of the constant of proportionality into the equation:
The answer is:
