To combine the expression \( \frac{a}{b} + \frac{a}{d} \) into a single fraction, you need to find a common denominator. The common denominator for the fractions \( b \) and \( d \) is \( bd \).
Now, rewrite each fraction with the common denominator:
\[ \frac{a}{b} = \frac{a \cdot d}{b \cdot d} = \frac{ad}{bd} \]
\[ \frac{a}{d} = \frac{a \cdot b}{d \cdot b} = \frac{ab}{bd} \]
Now, add the fractions:
\[ \frac{ad}{bd} + \frac{ab}{bd} = \frac{ad + ab}{bd} \]
So, the expression \( \frac{a}{b} + \frac{a}{d} \) as a simple fraction is:
\[ \frac{ad + ab}{bd} \]
You can also factor out \( a \) from the numerator:
\[ \frac{a(d + b)}{bd} \]
Thus, the final answer is:
\[ \frac{a(d + b)}{bd} \]