Question

giải phương trình
\(\dfrac{2x-1}{x^2-4x+4} + \dfrac{5x}{x-2} - \dfrac{25x}{5x-10} = 0\)

Answer 1

\(\dfrac{2x-1}{\left(x-2\right)^2}+\dfrac{5x}{x-2}-\dfrac{25x}{5\left(x-2\right)}=0\)

\(\Leftrightarrow\dfrac{\left(2x-1\right).5}{\left(x-2\right)^2.5}+\dfrac{5x\left(x-2\right).5}{\left(x-2\right).\left(x-2\right).5}-\dfrac{25x\left(x-2\right)}{5\left(x-2\right)\left(x-2\right)}=0\)

\(\Leftrightarrow\dfrac{10x-5+25x^2-50x-25x^2+50x}{5\left(x-2\right)^2}=0\)

\(\Leftrightarrow\dfrac{10x-5}{5\left(x-2\right)^2}=0\)

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

\(\Leftrightarrow\dfrac{2x-1}{x-2}=0\)

\(\Leftrightarrow x=\dfrac{1}{2}\)