a) x/x-3-6/x=18/x^2-3x

b) 3x-4/x^2-1-2/x+1=0

c) 2x+5/3+4-7x/2<8

Đáp án:

\(\begin{array}{l}
a)x = 6\\
b)x = 2\\
c)x >  - \dfrac{{26}}{{17}}
\end{array}\)

Giải thích các bước giải:

\(\begin{array}{l}
a)DK:x \ne \left\{ {0;3} \right\}\\
\dfrac{x}{{x - 3}} - \dfrac{6}{x} = \dfrac{{18}}{{{x^2} - 3x}}\\
 \to \dfrac{{{x^2} - 6\left( {x - 3} \right) - 18}}{{x\left( {x - 3} \right)}} = 0\\
 \to {x^2} - 6x + 18 - 18 = 0\\
 \to x\left( {x - 6} \right) = 0\\
 \to \left[ \begin{array}{l}
x = 0\left( l \right)\\
x = 6
\end{array} \right.\\
b)DK:x \ne  \pm 1\\
\dfrac{{3x - 4}}{{{x^2} - 1}} - \dfrac{2}{{x + 1}} = 0\\
 \to 3x - 4 - 2\left( {x - 1} \right) = 0\\
 \to 3x - 4 - 2x + 2 = 0\\
 \to x = 2\\
c)\dfrac{{2x + 5}}{3} + \dfrac{{4 - 7x}}{2} < 8\\
 \to \dfrac{{4x + 10 + 12 - 21x - 48}}{6} < 0\\
 \to  - 17x - 26 < 0\\
 \to x >  - \dfrac{{26}}{{17}}
\end{array}\)