To add these fractions, we first need to find a common denominator. The least common multiple of 8, 25, and 35 is 200.

So, we rewrite the fractions with a common denominator of 200:

-7/4 = -7 * 50/4 * 50 = -350/200
8/25 = 8 * 8/25 * 8 = 64/200
-21/35 = -21 * 5/35 * 5 = -105/200

Now, we can add the fractions:

-350/200 + 64/200 - 105/200 = -350 + 64 - 105 / 200 = -391/200

Therefore, the sum of -7/4, 8/25, and -21/35 is -391/200.