Question

mọi người giúp mình bài này với

giải phương trình: \(\dfrac{2x+1}{x-1}=\dfrac{5\left(x-1\right)}{x+1}\)

Answer 1

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

ĐKXĐ : \(x\ne1;x\ne-1\)

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

\(\Rightarrow\left(x+1\right)\left(2x+1\right)=\left(x-1\right)\left(5x-5\right)\)

\(\Leftrightarrow2x^2+x+2x+1=5x^2-5x-5x+5\)

\(\Leftrightarrow-3x^2+13x-4\)

\(\Leftrightarrow\left[{}\begin{matrix}x-4=0\\3x-1=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=4\\x=\dfrac{1}{3}\end{matrix}\right.\)

Vậy ................