Find \( f \) if \( \quad \frac{1}{f}=\frac{1}{v}+\frac{1}{u} \quad \) and \( v=3, u=7 \)

To find \( f \) given the equation \[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \] and substituting \( v = 3 \) and \( u = 7 \), we start by plugging in the values: \[ \frac{1}{f} = \frac{1}{3} + \frac{1}{7} \] Now, we need to find a common denominator to add the fractions on the right side. The least common multiple of 3 and 7 is 21. Therefore, we rewrite the fractions: \[ \frac{1}{3} = \frac{7}{21} \quad \text{and} \quad \frac{1}{7} = \frac{3}{21} \] Now, we can add these two fractions together: \[ \frac{1}{f} = \frac{7}{21} + \frac{3}{21} = \frac{10}{21} \] Now, we take the reciprocal to find \( f \): \[ f = \frac{21}{10} \] So, the final answer is \[ f = 2.1 \]