Question

\(\dfrac{100}{x-10}-\dfrac{100}{x}=\dfrac{1}{2}\)

Answer 1

\(\dfrac{100}{x-10}-\dfrac{100}{x}=\dfrac{1}{2}\)

\(\Rightarrow\dfrac{100x}{x^2-10}-\dfrac{100x-1000}{x^2-10}=\dfrac{1}{2}\)

\(\Rightarrow\dfrac{100x-100x+1000}{x^2-10}=\dfrac{1}{2}\)

\(\Rightarrow\dfrac{1000}{x^2-10}=\dfrac{1}{2}\)

\(\Rightarrow x^2-10=2000\)

\(\Rightarrow x^2=2010\Rightarrow x=\pm\sqrt{2010}\)