Simplify the given complex fraction: $\frac{\frac{x}{x+3}-\frac{3}{x}}{\frac{x}{x+3}+\frac{3}{x}}$

Step 1 ：The given expression is a complex fraction, which is a fraction where the numerator, the denominator, or both are fractions themselves. To simplify this, we can use the method of multiplying the numerator and the denominator by the least common denominator (LCD) of all the fractions in the expression. The LCD of the fractions in this case is \((x)(x+3)\).

Step 2 ：Let's denote the numerator as \(x/(x + 3) - 3/x\) and the denominator as \(x/(x + 3) + 3/x\).

Step 3 ：By multiplying the numerator and the denominator by the LCD, we get the simplified expression as \((x^2 - 3x - 9)/(x^2 + 3x + 9)\).

Step 4 ：Final Answer: The simplified form of the given complex fraction is \(\boxed{\frac{x^2 - 3x - 9}{x^2 + 3x + 9}}\).