Add. \[ \frac{3}{4}+\frac{7}{9} \] Write your answer as a fraction in simplest form.

To add the fractions \(\frac{3}{4}\) and \(\frac{7}{9}\), we first need to find a common denominator. The least common multiple (LCM) of 4 and 9 is 36. Next, we convert each fraction: \[ \frac{3}{4} = \frac{3 \times 9}{4 \times 9} = \frac{27}{36} \] \[ \frac{7}{9} = \frac{7 \times 4}{9 \times 4} = \frac{28}{36} \] Now, add the two fractions: \[ \frac{27}{36} + \frac{28}{36} = \frac{27 + 28}{36} = \frac{55}{36} \] The fraction \(\frac{55}{36}\) is already in its simplest form (55 and 36 have no common factors other than 1). Therefore, the answer is \[ \frac{55}{36} \]