Toán Lớp 8: Tính : 1/(x-1) – 1/(x-1)(2-x) + 1/(x-2)(x-3)
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Toán Lớp 8: Tính : 1/(x-1) – 1/(x-1)(2-x) + 1/(x-2)(x-3)
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DK:x \ne \left\{ {1;2;3} \right\}\\
\dfrac{1}{{x – 1}} – \dfrac{1}{{\left( {x – 1} \right)\left( {2 – x} \right)}} + \dfrac{1}{{\left( {x – 2} \right)\left( {x – 3} \right)}}\\
= \dfrac{{\left( {x – 2} \right)\left( {x – 3} \right) + x – 3 + x – 1}}{{\left( {x – 2} \right)\left( {x – 3} \right)\left( {x – 1} \right)}}\\
= \dfrac{{{x^2} – 5x + 6 + 2x – 4}}{{\left( {x – 2} \right)\left( {x – 3} \right)\left( {x – 1} \right)}}\\
= \dfrac{{{x^2} – 3x + 2}}{{\left( {x – 2} \right)\left( {x – 3} \right)\left( {x – 1} \right)}}\\
= \dfrac{{{x^2} – x – 2x + 2}}{{\left( {x – 2} \right)\left( {x – 3} \right)\left( {x – 1} \right)}}\\
= \dfrac{{x\left( {x – 1} \right) – 2\left( {x – 1} \right)}}{{\left( {x – 2} \right)\left( {x – 3} \right)\left( {x – 1} \right)}}\\
= \dfrac{{\left( {x – 1} \right)\left( {x – 2} \right)}}{{\left( {x – 2} \right)\left( {x – 3} \right)\left( {x – 1} \right)}}\\
= \dfrac{1}{{x – 3}}
\end{array}\)