\(=\dfrac{3\left(\dfrac{1}{1}+\dfrac{1}{3}+\dfrac{1}{5}+...+\dfrac{1}{99}\right)}{\dfrac{1}{100}\left(\dfrac{100}{1\cdot99}+\dfrac{100}{3\cdot97}+...+\dfrac{100}{99\cdot1}\right)}\)
\(=\dfrac{3\left(1+\dfrac{1}{3}+\dfrac{1}{5}+...+\dfrac{1}{99}\right)}{\dfrac{1}{100}\cdot\left(\dfrac{1}{1}+\dfrac{1}{99}+\dfrac{1}{3}+\dfrac{1}{97}+...+\dfrac{1}{99}+\dfrac{1}{1}\right)}\)
\(=\dfrac{3\left(1+\dfrac{1}{3}+\dfrac{1}{5}+...+\dfrac{1}{99}\right)}{\dfrac{1}{50}\left(1+\dfrac{1}{3}+\dfrac{1}{5}+...+\dfrac{1}{99}\right)}=3:\dfrac{1}{50}=150\)