Simplify the complex fraction. \[ \frac{\frac{r}{s}-1}{\frac{r}{s}+1} \]

Step 1 ：Given the complex fraction \(\frac{\frac{r}{s}-1}{\frac{r}{s}+1}\)

Step 2 ：The first step to simplify this complex fraction is to get rid of the fraction in the numerator and denominator. We can do this by multiplying the numerator and denominator by s, which gives us \(\frac{s^2*(r/s - 1)}{r/s + 1}\)

Step 3 ：Simplifying the expression, we get \(\frac{s^2*(r - s)}{r + s}\)

Step 4 ：The expression can be further simplified by cancelling out the common factor of s in the numerator and denominator, which gives us \(\frac{r*s^2 - s^3}{r + s}\)

Step 5 ：Final Answer: The simplified form of the complex fraction is \(\boxed{\frac{r s^2 - s^3}{r + s}}\)