Giải phương trình: 2x/(x - 2) + 5/(3 - x) = 5/(c^2 - 5x + 6)
Giải phương trình: \[\frac{{2x}}{{x - 2}} + \frac{5}{{3 - x}} = \frac{5}{{{x^2} - 5x + 6}}\]
Đkxđ: \[x \ne 2,\,\,x \ne 3\]
\[\frac{{2x}}{{x - 2}} + \frac{5}{{3 - x}} = \frac{5}{{{x^2} - 5x + 6}}\]
\[ \Leftrightarrow \frac{{2x(x - 3)}}{{(x - 2)(x - 3)}}\frac{{5(x - 2)}}{{(x - 2)(x - 3)}}\frac{5}{{(x - 2)(x - 3)}} = 0\]
\[ \Leftrightarrow \frac{{2{x^2} - 6x - 5x + 10}}{{(x - 2)(x - 3)}} = 0\]
\[ \Rightarrow 2{x^2} - 11x + 5 = 0\]
\[ \Leftrightarrow (2{x^2} - 10x) - (x - 5) = 0\]
\[ \Leftrightarrow 2x(x - 5) - (x - 5) = 0\]
\[ \Leftrightarrow (x - 5)(2x - 1) = 0\]
\[ \Leftrightarrow \left[ \begin{array}{l}x = 5(tm)\\x = \frac{1}{2}(tm)\end{array} \right.\]
Vậy \[x = \left\{ {5;\,\,\frac{1}{2}} \right\}\]