دانلود اپلیکیشن
معادلهٔ \(\frac{{x - 2}}{{x - 5}} + \frac{{x - 1}}{{x + 4}} = \frac{{{x^2} - 6x + 5}}{{{x^2} - x - 20}}\) را حل کنید.
حل:
\(\begin{array}{l}\frac{{x - 2}}{{x - 5}} + \frac{{x - 1}}{{x + 4}} - \frac{{{x^2} - 6x + 5}}{{{x^2} - x - 20}} = 0\\\\ \Rightarrow \frac{{(x - 2)(..........)}}{{(x - 5)(..........)}} + \frac{{(x - 1)(..........)}}{{(x + 4)(..........)}} - \frac{{{x^2} - 6x + 5}}{{(x - 5)(x + 4)}} = 0\\\\ \Rightarrow \frac{{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}}{{(x - 5)(x + 4)}} = 0 \Rightarrow ............. = 0 \Rightarrow ..........\end{array}\)
\(\begin{array}{l}\frac{{x - 2}}{{x - 5}} + \frac{{x - 1}}{{x + 4}} - \frac{{{x^2} - 6x + 5}}{{{x^2} - x - 20}} = 0\\\\ \Rightarrow \frac{{(x - 2)(x + 4)}}{{(x - 5)(x + 4)}} + \frac{{(x - 1)(x - 5)}}{{(x + 4)(x - 5)}} - \frac{{{x^2} - 6x + 5}}{{(x - 5)(x + 4)}} = 0\\\\ \Rightarrow \frac{{{x^2} + 2x - 8 + {x^2} - 6x + 5 - {x^2} + 6x - 5}}{{(x - 5)(x + 4)}} = 0\\\\ \Rightarrow \frac{{{x^2} + 2x - 8}}{{(x - 5)(x + 4)}} = 0 \Rightarrow {x^2} + 2x - 8 = 0\\\\ \Rightarrow (x - 2)(x + 4) = 0 \Rightarrow \left\{ \begin{array}{l}x = 2\\\\x = - 4\end{array} \right.\end{array}\)
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