*Giải phương trình ấn của mẫu: c, (1/x-1)-(2x/x^2+x+1)=(3x^2/x^3-1) d, 2x-(4x/x+3)=(2x^2/x+3)+2/7

Đáp án:

$\begin{array}{l}
Dk:x \ne 1\\
\dfrac{1}{{x - 1}} - \dfrac{{2x}}{{{x^2} + x + 1}} = \dfrac{{3{x^2}}}{{{x^3} - 1}}\\
 \Leftrightarrow \dfrac{{{x^2} + x + 1 - 2x\left( {x - 1} \right)}}{{\left( {x - 1} \right)\left( {{x^2} + x + 1} \right)}} = \dfrac{{3{x^2}}}{{\left( {x - 1} \right)\left( {{x^2} + x + 1} \right)}}\\
 \Leftrightarrow {x^2} + x + 1 - 2{x^2} + 2x = 3{x^2}\\
 \Leftrightarrow  - {x^2} + 3x + 1 = 3{x^2}\\
 \Leftrightarrow 4{x^2} - 3x - 1 = 0\\
 \Leftrightarrow \left( {4x + 1} \right)\left( {x - 1} \right) = 0\\
 \Leftrightarrow x =  - \dfrac{1}{4}\left( {tm} \right)\left( {do:x \ne 1} \right)\\
Vậy\,x =  - \dfrac{1}{4}\\
d)Dk:x \ne  - 3\\
2x - \dfrac{{4x}}{{x + 3}} = \dfrac{{2{x^2}}}{{x + 3}} + \dfrac{2}{7}\\
 \Leftrightarrow \dfrac{{2x.7.\left( {x + 3} \right) - 4x.7}}{{7\left( {x + 3} \right)}} = \dfrac{{7.2{x^2} + 2\left( {x + 3} \right)}}{{7\left( {x + 3} \right)}}\\
 \Leftrightarrow 14{x^2} + 42x - 28x = 14{x^2} + 2x + 6\\
 \Leftrightarrow 12x = 6\\
 \Leftrightarrow x = \dfrac{1}{2}\left( {tm} \right)\\
Vậy\,x = \dfrac{1}{2}
\end{array}$