To add these fractions, we need to find a common denominator. The least common multiple of 18 and 35 is 630.

Now, we can rewrite the fractions with the common denominator:

12/18 = (12 * 35)/(18 * 35) = 420/630
21/35 = (21 * 18)/(35 * 18) = 378/630

Now, we can add the fractions:

420/630 + 378/630 = (420 + 378)/630 = 798/630

To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 6:

798/630 = (798 ÷ 6)/(630 ÷ 6) = 133/105

Therefore, 12/18 + 21/35 = 133/105.