Question

Answer 1

\(\dfrac{1}{\left(x-2\right)\left(x-3\right)}+\dfrac{1}{\left(x-3\right)\left(x-4\right)}-\dfrac{x}{\left(x-5\right)\left(x-4\right)}=0\)

\(\Leftrightarrow\dfrac{1}{x-2}-\dfrac{1}{x-3}+\dfrac{1}{x-3}-\dfrac{1}{x-4}-\dfrac{x}{\left(x-4\right)\left(x-5\right)}=0\)

\(\Leftrightarrow\dfrac{x-4-x+2}{\left(x-2\right)\left(x-4\right)}-\dfrac{x}{\left(x-4\right)\left(x-5\right)}=0\)

\(\Rightarrow-2\left(x-5\right)-x\left(x-2\right)=0\Leftrightarrow-x^2-4x+10=0\)

\(\Leftrightarrow x=-2\pm\sqrt{14}\)