Question

x-3/x-2-x-2/x-4=3/1/5

Answer 1

\(\dfrac{x-3}{x-2}-2-\dfrac{x-2}{x-4}=\dfrac{3}{\dfrac{1}{5}}=15\)

\(\Leftrightarrow\dfrac{\left(x-3\right)\left(x-4\right)}{\left(x-2\right)\left(x-4\right)}-\dfrac{2\left(x-2\right)\left(x-4\right)}{\left(x-2\right)\left(x-4\right)}-\dfrac{15\left(x-2\right)\left(x-4\right)}{\left(x-2\right)\left(x-4\right)}=0\)

\(\Leftrightarrow\left(x-3\right)\left(x-4\right)-2\left(x-2\right)\left(x-4\right)-15\left(x-2\right)\left(x-4\right)=0\)

\(\Leftrightarrow\left(x-3\right)\left(x-4\right)-\left(2x-4\right)\left(x-4\right)-\left(15x-30\right)\left(x-4\right)=0\)

\(\Leftrightarrow\left(x-4\right)\left(x-3-2x+4-15x+30\right)=0\)

\(\Leftrightarrow\left(x-4\right)\left(31-16x\right)=0\)

\(\Leftrightarrow\left\{{}\begin{matrix}x-4=0\\31-16x=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=4\\x=\dfrac{31}{16}\end{matrix}\right.\)