Combine the following fractions and express in fully reduced form. \[ \frac{7 x}{6}+\frac{9 x}{4} \]

To combine the fractions \( \frac{7 x}{6} + \frac{9 x}{4} \), we need a common denominator. The least common multiple of 6 and 4 is 12. Now, convert each fraction: 1. For \( \frac{7 x}{6} \): \[ \frac{7 x}{6} = \frac{7 x \cdot 2}{6 \cdot 2} = \frac{14 x}{12} \] 2. For \( \frac{9 x}{4} \): \[ \frac{9 x}{4} = \frac{9 x \cdot 3}{4 \cdot 3} = \frac{27 x}{12} \] Now we can add the two fractions: \[ \frac{14 x}{12} + \frac{27 x}{12} = \frac{14 x + 27 x}{12} = \frac{41 x}{12} \] Finally, \( \frac{41 x}{12} \) is already in fully reduced form since 41 is a prime number and does not share any factors with 12. So, the final answer is: \[ \frac{41 x}{12} \]