Draw a rough image of f(x) first, and distinguish it from the image, and draw it as follows.

When x tends to negative infinity, f(x) tends to-1;

When x tends to the left of b, 1/x-b tends to negative infinity, so f(x) tends to negative infinity;

When x tends to the right of b, 1/x-b tends to positive infinity, so f(x) tends to positive infinity;

When x tends to the left of a, 1/x-b tends to negative infinity, so f(x) tends to negative infinity;

When x tends to the right of a, 1/x-b tends to positive infinity, so f(x) tends to positive infinity;

When x tends to positive infinity, f(x) tends to negative infinity.

When x is in the interval of (b, a), f(x) is continuous, ranging from positive infinity to negative infinity, so there must be a zero point of X 1;

When x is greater than a, f(x) is continuous, ranging from positive infinity to negative infinity, so there must be a zero in X2.

There can't be other zeros, so it's B.