Question

( 45/x-5 )- ( 45/x) = 3/2

Answer 1

\(\dfrac{45}{x-5}-\dfrac{45}{x}=\dfrac{3}{2}\\ \Leftrightarrow\dfrac{1}{x-5}-\dfrac{1}{x}=\dfrac{1}{30}\\ \Leftrightarrow\dfrac{x-\left(x-5\right)}{x\left(x-5\right)}=\dfrac{1}{30}\\ \Leftrightarrow\dfrac{5}{x^2-5x}=\dfrac{1}{30}\\ \Leftrightarrow x^2-5x=600\\ \Leftrightarrow x^2-5x-150=0\\ \Leftrightarrow\left(x+10\right)\left(x-15\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=-10\\x=15\end{matrix}\right.\left(t.m\right)}\)