Simplify. \[ \frac{a-\frac{9}{a}}{\frac{9}{a}+a} \]

Step 1 ：Given the expression \(\frac{a-\frac{9}{a}}{\frac{9}{a}+a}\)

Step 2 ：To simplify this expression, we can multiply the numerator and the denominator by 'a' to get rid of the fractions.

Step 3 ：This gives us \(\frac{a^2 - 9}{a^2 + 9}\)

Step 4 ：Final Answer: The simplified form of the given expression is \(\boxed{\frac{a^2 - 9}{a^2 + 9}}\)