How many solutions does the equation \( \frac{(x-1)(x-2)(x-3)\dotsm(x-100)}{(x-1^2)(x-2^2)(x-3^2)\dotsm(x-100^2)} = 0\) have for \(x\)?
The equation simplifies to:
\((x-1)(x-2)(x-3) \dots (x-100) = 0\)
There are 100 solutions, namely x = 1 to x = 100.