Câu hỏi/bài tập:
Rút gọn biểu thức \(P = \frac{3}{{\left( {x + 1} \right)\left( {x + 4} \right)}} - \frac{1}{{\left( {x + 2} \right)\left( {x + 3} \right)}} - \frac{1}{{\left( {x + 2} \right)\left( {x + 1} \right)}}\).
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Rút gọn biểu thức \(P = \frac{3}{{\left( {x + 1} \right)\left( {x + 4} \right)}} - \frac{1}{{\left( {x + 2} \right)\left( {x + 3} \right)}} - \frac{1}{{\left( {x + 2} \right)\left( {x + 1} \right)}}\).
\(\begin{array}{l}P = \frac{3}{{\left( {x + 1} \right)\left( {x + 4} \right)}} - \frac{1}{{\left( {x + 2} \right)\left( {x + 3} \right)}} - \frac{1}{{\left( {x + 2} \right)\left( {x + 1} \right)}}\\ = \frac{3}{{\left( {x + 1} \right)\left( {x + 4} \right)}} - \left( {\frac{1}{{\left( {x + 2} \right)\left( {x + 3} \right)}} + \frac{1}{{\left( {x + 2} \right)\left( {x + 1} \right)}}} \right)\\ = \frac{3}{{\left( {x + 1} \right)\left( {x + 4} \right)}} - \frac{{x + 1 - (x + 3)}}{{(x + 1)(x + 3)}}\\ = \frac{3}{{\left( {x + 1} \right)\left( {x + 4} \right)}} - \frac{2}{{\left( {x + 1} \right)\left( {x + 3} \right)}}\\ = \frac{{3\left( {x + 3} \right)}}{{\left( {x + 1} \right)\left( {x + 3} \right)\left( {x + 4} \right)}} - \frac{{2\left( {x + 4} \right)}}{{\left( {x + 1} \right)\left( {x + 3} \right)\left( {x + 4} \right)}}\\ = \frac{{x + 1}}{{\left( {x + 1} \right)\left( {x + 3} \right)\left( {x + 4} \right)}} = \frac{1}{{\left( {x + 3} \right)\left( {x + 4} \right)}}\end{array}\)