Giải phương trình: x-1/x+2 – x-2/x+3 – x-4/x+5 + x-5/x+6 = 0 02/08/2021 Bởi Abigail Giải phương trình: x-1/x+2 – x-2/x+3 – x-4/x+5 + x-5/x+6 = 0
Đáp án: \[\left[ \begin{array}{l}x = – \frac{1}{2}\\x = – 4\end{array} \right.\] Giải thích các bước giải: ĐKXĐ: \(\left\{ \begin{array}{l}x \ne – 2\\x \ne – 3\\x \ne – 5\\x \ne – 6\end{array} \right.\) Ta có; \[\begin{array}{l}\frac{{x – 1}}{{x + 2}} – \frac{{x – 2}}{{x + 3}} – \frac{{x – 4}}{{x + 5}} + \frac{{x – 5}}{{x + 6}} = 0\\ \Leftrightarrow \frac{{\left( {x – 1} \right)\left( {x + 3} \right) – \left( {x – 2} \right)\left( {x + 2} \right)}}{{\left( {x + 2} \right)\left( {x + 3} \right)}} – \frac{{\left( {x – 4} \right)\left( {x + 6} \right) – \left( {x – 5} \right)\left( {x + 5} \right)}}{{\left( {x + 5} \right)\left( {x + 6} \right)}} = 0\\ \Leftrightarrow \frac{{{x^2} + 2x – 3 – {x^2} + 4}}{{{x^2} + 5x + 6}} – \frac{{{x^2} + 2x – 24 – {x^2} + 25}}{{{x^2} + 11x + 30}} = 0\\ \Leftrightarrow \frac{{2x + 1}}{{{x^2} + 5x + 6}} – \frac{{2x + 1}}{{{x^2} + 11x + 30}} = 0\\ \Leftrightarrow \left[ \begin{array}{l}2x + 1 = 0\\{x^2} + 5x + 6 = {x^2} + 11x + 30\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}x = – \frac{1}{2}\\x = – 4\end{array} \right.\end{array}\] Bình luận
Đáp án:
\[\left[ \begin{array}{l}
x = – \frac{1}{2}\\
x = – 4
\end{array} \right.\]
Giải thích các bước giải:
ĐKXĐ: \(\left\{ \begin{array}{l}
x \ne – 2\\
x \ne – 3\\
x \ne – 5\\
x \ne – 6
\end{array} \right.\)
Ta có;
\[\begin{array}{l}
\frac{{x – 1}}{{x + 2}} – \frac{{x – 2}}{{x + 3}} – \frac{{x – 4}}{{x + 5}} + \frac{{x – 5}}{{x + 6}} = 0\\
\Leftrightarrow \frac{{\left( {x – 1} \right)\left( {x + 3} \right) – \left( {x – 2} \right)\left( {x + 2} \right)}}{{\left( {x + 2} \right)\left( {x + 3} \right)}} – \frac{{\left( {x – 4} \right)\left( {x + 6} \right) – \left( {x – 5} \right)\left( {x + 5} \right)}}{{\left( {x + 5} \right)\left( {x + 6} \right)}} = 0\\
\Leftrightarrow \frac{{{x^2} + 2x – 3 – {x^2} + 4}}{{{x^2} + 5x + 6}} – \frac{{{x^2} + 2x – 24 – {x^2} + 25}}{{{x^2} + 11x + 30}} = 0\\
\Leftrightarrow \frac{{2x + 1}}{{{x^2} + 5x + 6}} – \frac{{2x + 1}}{{{x^2} + 11x + 30}} = 0\\
\Leftrightarrow \left[ \begin{array}{l}
2x + 1 = 0\\
{x^2} + 5x + 6 = {x^2} + 11x + 30
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = – \frac{1}{2}\\
x = – 4
\end{array} \right.
\end{array}\]