First, let's convert the mixed number to an improper fraction:
3/4 + 3 + 1/9 × 3/7
= 3/4 + 3 + 1/(97) 3
= 3/4 + 3 + 1/63 * 3

Next, let's find a common denominator for 3/4 and 3:
3/4 = 9/12
So now we have:
9/12 + 3 + 1/63 * 3

Now let's add the fractions:
9/12 + 3 + 1/63 * 3
= 9/12 + 36/12 + 3/63
= 45/12 + 3/63
= 135/36 + 4/36
= 139/36

Therefore, the final answer is 139/36.