If f(x)= x-B/x-A, f(2)=0, and f(1) is undefined, what are the calues of A and B?

my teacher is picky and requires all work to be shown. can you explain how you got this answer?

A is 1 from the f(1) is zero. The denominator has to be zero.
B is two, since A is one, and f(2) is 0

To find the values of A and B, we need to evaluate the given information. Let's start by considering the given function:

f(x) = (x - B)/(x - A)

We are given that f(2) = 0, which means we need to substitute x = 2 into the function and solve for A and B:

0 = (2 - B)/(2 - A)

Multiplying both sides by (2 - A), we get:

0 = 2 - B

Subtracting 2 from both sides gives us:

-2 = -B

Simplifying, we find:

B = 2

Now, let's move on to finding the value of A. We are given that f(1) is undefined, which means the denominator of the function, (x - A), must be zero when x = 1:

1 - A = 0

Solving for A, we get:

A = 1

Therefore, the values of A and B are A = 1 and B = 2, respectively.