3x+2/2-6x+1/6=5/3+2x Giúp em vs nhanh nha Giải pt

Đáp án:

\(\left[ \begin{array}{l}
x = \frac{{ – 41 + 3\sqrt {201} }}{{12}}\\
x = \frac{{ – 41 – 3\sqrt {201} }}{{12}}
\end{array} \right.\)

Giải thích các bước giải:

\(\begin{array}{l}
DK:x \ne \left\{ { – \frac{3}{2};\frac{1}{3}} \right\}\\
\frac{{3x + 2}}{{2 – 6x}} + \frac{1}{6} = \frac{5}{{3 + 2x}}\\
 \to \frac{{6{{\left( {3x + 2} \right)}^2} + \left( {2 – 6x} \right)\left( {3x + 2} \right) – 5.6.\left( {2 – 6x} \right)}}{{6\left( {2 – 6x} \right)\left( {3x + 2} \right)}} = 0\\
 \to 6\left( {9{x^2} + 12x + 4} \right) – 18{x^2} – 6x + 4 – 60 + 180x = 0\\
 \to 36{x^2} + 246x – 32 = 0\\
Do: Δ’= {123^2} + 36.32 = 16281 > 0\\
 \to \left[ \begin{array}{l}
x = \frac{{ – 41 + 3\sqrt {201} }}{{12}}\\
x = \frac{{ – 41 – 3\sqrt {201} }}{{12}}
\end{array} \right.
\end{array}\)