3. (10 points) The sum and the quotient of two numbers are both 6, then the product of these two numbers minus the difference of these two numbers (larger minus smaller) equals ( )
A. $26 \frac{4}{7}$
B. $5 \frac{1}{7}$
C. $\frac{6}{7}$
D. $\frac{6}{49}$
【Analysis】According to the problem, the larger number can be called A, and the smaller number can be called B. From the problem, we know that A is 6 times B, and A plus B equals 6. Using the sum-multiple formula, we can find that B is $6 \div(6+1)=\frac{6}{7}$, and then according to the problem, we can find A, and then we can find the product and difference of these two numbers, and then subtract them.

【Solution】Solution: Let the larger number be A, and the smaller number be B.
From the difference-multiple formula, we get B is: $6 \div(6+1)=\frac{6}{7}$,
Then A is: $\frac{6}{7} \times 6=\frac{36}{7}$;
The product of the two numbers is: $\frac{6}{7} \times \frac{36}{7}=\frac{216}{49}$,
The difference between the two numbers is: $\frac{36}{7}-\frac{6}{7}=\frac{30}{7}=\frac{210}{49}$,
Then: $\frac{216}{49}-\frac{210}{49}=\frac{6}{49}$;
Therefore, the answer is: $D$.