\(\dfrac{1}{{x + 1}} - \dfrac{{x - 1}}{x} = \dfrac{{3x + 1}}{{x\left( {x + 1} \right)}}\)
ĐKXĐ: \(x \ne 0;x \ne - 1\)
\( \Leftrightarrow x - \left( {x - 1} \right)\left( {x + 1} \right) = 3x + 1\\ \Leftrightarrow x - \left( {{x^2} - 1} \right) = 3x + 1\\ \Leftrightarrow x - {x^2} + 1 = 3x + 1\\ \Leftrightarrow - {x^2} - 2x = 0\\ \Leftrightarrow x\left( { - x - 2} \right) = 0\\ \Leftrightarrow \left[ \begin{array}{l} x = 0\\ - x - 2 = 0 \end{array} \right. \Leftrightarrow \left[ \begin{array}{l} x = 0 (ktm)\\ x = - 2(tm) \end{array} \right. \)
\(\frac{1}{x+1}\)-\(\frac{x-1}{x}\)=\(\frac{3x+1}{x\left(x+1\right)}\)
ĐKXĐ: x\(\ne\)0; x\(\ne\)-1
\(\Leftrightarrow\frac{x}{\left(x+1\right).x}\)-\(\frac{\left(x-1\right).\left(x+1\right)}{x\left(x+1\right)}\)=\(\frac{3x+1}{x\left(x+1\right)}\)
\(\Leftrightarrow\) x - x2 +x-x-1 = 3x+1
\(\Leftrightarrow\) -x2 - 2x=0
\(\Leftrightarrow\) x(-x-2)=0
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\-x-2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\left(loại\right)\\-x=2\Rightarrow x=-2\left(nhận\right)\end{matrix}\right.\)
