Giải:
\(\dfrac{14}{3x-12}-\dfrac{2+x}{x-4}=\dfrac{3}{8-2x}-\dfrac{5}{6}\)
\(\Leftrightarrow\dfrac{14}{3\left(x-4\right)}-\dfrac{2+x}{x-4}=\dfrac{3}{2\left(4-x\right)}-\dfrac{5}{6}\) (1)
ĐKXĐ: \(x\ne4\)
\(\left(1\right)\Leftrightarrow\dfrac{14.2}{2.3.\left(x-4\right)}-\dfrac{2.3.\left(2+x\right)}{2.3.\left(x-4\right)}=\dfrac{-3.3}{2.3.\left(x-4\right)}-\dfrac{5.\left(x-4\right)}{2.3.\left(x-4\right)}\)
\(\Rightarrow14.2-2.3.\left(2+x\right)=-3.3-5.\left(x-4\right)\)
\(\Leftrightarrow28-6\left(2+x\right)=-9-5\left(x-4\right)\)
\(\Leftrightarrow28-12-6x=-9-5x+20\)
\(\Leftrightarrow-6x+5x=-9+20-28+12\)
\(\Leftrightarrow-x=-5\)
\(\Leftrightarrow x=5\) ( Thỏa mãn ĐKXĐ)
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