Bài giải:

$\frac{2x+1}{x-1}=\frac{5(x-1)}{x+1}$

ĐKXĐ: x $\ne $1; x $\ne $-1

$\Leftrightarrow \frac{(2x+1)(x+1)}{(x-1)(x+1)}=\frac{5(x-1)(x-1)}{(x+1)(x-1)}$

$\Leftrightarrow $2x² + 3x +  1 = 5x² – 10x + 5

$\Leftrightarrow $-3x² + 13x – 4 = 0

$\Leftrightarrow $(3x – 1)(x – 4) = 0

$\Leftrightarrow \left[ \begin{align}& 3x-1=0 \\ & x-4=0 \\ \end{align} \right.$

$\Leftrightarrow \left[ \begin{align}& x=\frac{1}{3} \\ & x=4 \\ \end{align} \right.$            (thỏa mãn)

Vậy đáp án đúng là: C