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Giải bài 6 trang 17 vở thực hành Toán 8 tập 2

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)}}).

♓Tổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Kết nối tri thức

Toán - Văn - Anh - Khoa học tự nhiên
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Đề bài

🦹Rút gọn biểu thức \(P = \frac{3}{{\left( {x + 1} \right)\left( {x + 4} \right)}} - \frac{1}{{\left( {x + 2} \right)\left( {x + 3} \right)}} - \frac{1}{{\left( {x + 2} \right)\left( {x + 1} \right)}}\).

Phương pháp giải - Xem chi tiết

Sử dụng đẳng thức $\frac{1}{a(a+1)}=\frac{1}{a}-\frac{1}{a+1}$

Lời giải chi tiết

꧂\(\begin{array}{l}P = \frac{3}{{\left( {x + 1} \right)\left( {x + 4} \right)}} - \frac{1}{{\left( {x + 2} \right)\left( {x + 3} \right)}} - \frac{1}{{\left( {x + 2} \right)\left( {x + 1} \right)}}\\ = \frac{3}{{\left( {x + 1} \right)\left( {x + 4} \right)}} - \left( {\frac{1}{{\left( {x + 2} \right)\left( {x + 3} \right)}} + \frac{1}{{\left( {x + 2} \right)\left( {x + 1} \right)}}} \right)\\ = \frac{3}{{\left( {x + 1} \right)\left( {x + 4} \right)}} - \frac{{x + 1 - (x + 3)}}{{(x + 1)(x + 3)}}\\ = \frac{3}{{\left( {x + 1} \right)\left( {x + 4} \right)}} - \frac{2}{{\left( {x + 1} \right)\left( {x + 3} \right)}}\\ = \frac{{3\left( {x + 3} \right)}}{{\left( {x + 1} \right)\left( {x + 3} \right)\left( {x + 4} \right)}} - \frac{{2\left( {x + 4} \right)}}{{\left( {x + 1} \right)\left( {x + 3} \right)\left( {x + 4} \right)}}\\ = \frac{{x + 1}}{{\left( {x + 1} \right)\left( {x + 3} \right)\left( {x + 4} \right)}} = \frac{1}{{\left( {x + 3} \right)\left( {x + 4} \right)}}\end{array}\)

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