The trick here - apart from the usual one, of finding a common denominator - is to "lend" one from the whole part, and add it to the fraction. Since one whole is 3/4, you add 4/4, to get 7/4. Then (and after converting everything to the common denominator), you can easily subtract the fractional part.
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3 over 4
3 4/7 minus 1/7 is 3 3/7
1 whole and 1 over 10
The answer is 1/4. 1 whole would be 4/4 (4 over 4) so subtracting 3/4 (3 over 4) gives the result.
42/3 - 14/5 = 43/15 or 213/15