Toán Lớp 8: x/x-1-x+1/X^2-x bài 4: cho biểu thức Q=x+3/2x+1-x-7/2x+1
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Toán Lớp 8: x/x-1-x+1/X^2-x bài 4: cho biểu thức Q=x+3/2x+1-x-7/2x+1
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a)\dfrac{1}{{x\left( {x – 1} \right)}}\\
b)\left[ \begin{array}{l}
x = 2\\
x = – 3\\
x = 0\\
x = – 1
\end{array} \right.
\end{array}\)
a)DK:x \ne \left\{ {0;1} \right\}\\
\dfrac{x}{{x – 1}} – \dfrac{{x + 1}}{{{x^2} – x}}\\
= \dfrac{{{x^2} – \left( {x + 1} \right)\left( {x – 1} \right)}}{{x\left( {x – 1} \right)}}\\
= \dfrac{{{x^2} – {x^2} + 1}}{{x\left( {x – 1} \right)}}\\
= \dfrac{1}{{x\left( {x – 1} \right)}}\\
b)DK:x \ne – \dfrac{1}{2}\\
Q = \dfrac{{x + 3}}{{2x + 1}} – \dfrac{{x – 7}}{{2x + 1}}\\
= \dfrac{{x + 3 – x + 7}}{{2x + 1}}\\
= \dfrac{{10}}{{2x + 1}}\\
Q \in Z \to \dfrac{{10}}{{2x + 1}} \in Z\\
\to 2x + 1 \in U\left( {10} \right)\\
\to \left[ \begin{array}{l}
2x + 1 = 10\\
2x + 1 = – 10\\
2x + 1 = 5\\
2x + 1 = – 5\\
2x + 1 = 1\\
2x + 1 = – 1
\end{array} \right. \to \left[ \begin{array}{l}
x = \dfrac{9}{2}\left( l \right)\\
x = – \dfrac{{11}}{2}\left( l \right)\\
x = 2\\
x = – 3\\
x = 0\\
x = – 1
\end{array} \right.
\end{array}\)