The difference of a proper fraction and its reciprocal is $\frac{7}{12}$. Find the fraction.

A proper fraction $f$ satisfies $0<f<1$. Its reciprocal $\frac{1}{f}$ will therefore be greater than $1$. The positive difference between the reciprocal and the proper fraction is given as $\frac{7}{12}$:
$$\frac{1}{f}-f=\frac{7}{12}$$

Let us test Option B, where $f=\frac{3}{4}$:

* Reciprocal $=\frac{4}{3}$

Evaluating the difference:

$$\text{Difference}=\frac{4}{3}-\frac{3}{4}=\frac{16-9}{12}=\frac{7}{12}$$

This satisfies the given condition.