Rút gọn:
\(C=\left[\left(1+\dfrac{1}{x}\right)\cdot\dfrac{2}{x^3+3x^2+3x+1}+\left(1+\dfrac{1}{x^2}\right)\cdot\dfrac{1}{1+2x+x^2}\right]:\dfrac{x-1}{x^3}\)
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Những câu hỏi liên quan
9 tháng 5 2023
a: \(P=\left(\dfrac{3x+6}{2\left(x^2+4\right)}-\dfrac{2x^2-x-10}{\left(x+1\right)\left(x^2+1\right)}\right):\left(\dfrac{10\left(x^2-1\right)+3\left(x^2+1\right)\left(x-1\right)-6\left(x+1\right)\left(x^2+1\right)}{\left(x^2+1\right)\left(x+1\right)\left(x-1\right)\cdot2}\right)\cdot\dfrac{2}{x-1}\)
\(=\left(\dfrac{\left(3x+6\right)\left(x^3+x^2+x+1\right)-\left(2x^2+8\right)\left(2x^2-x-10\right)}{2\left(x^2+4\right)\left(x+1\right)\left(x^2+1\right)}\right)\cdot\dfrac{\left(x^2+1\right)\left(x-1\right)\left(x+1\right)\cdot2}{-3x^3+x^2-3x-13}\cdot\dfrac{2}{x-1}\)
\(=\dfrac{-x^4+11x^3+13x^2+17x+16}{\left(x^2+4\right)}\cdot\dfrac{2}{-3x^3+x^2-3x-13}\)
11 tháng 6 2022
\(=\dfrac{x^2-x+1-3+3x+3}{\left(x+1\right)\left(x^2-x+1\right)}\cdot\dfrac{3\left(x^2-x+1\right)}{\left(x+1\right)\left(x+2\right)}-\dfrac{2x-2}{x\left(x+2\right)}\)
\(=\dfrac{x^2+2x+1}{x+1}\cdot\dfrac{3}{\left(x+1\right)\left(x+2\right)}-\dfrac{2x-2}{x\left(x+2\right)}\)
\(=\dfrac{3}{x+2}-\dfrac{2x-2}{x\left(x+2\right)}=\dfrac{3x-2x+2}{x\left(x+2\right)}=\dfrac{1}{x}\)
PN
13 tháng 7 2017
Bài 1:
\(\left(-\dfrac{72}{40}-\dfrac{144}{60}-2\dfrac{1}{3}\right):\left(\dfrac{45}{100}-\dfrac{25}{60}+-\dfrac{75}{25}\right)\)
\(=\left(-\dfrac{9}{5}-\dfrac{12}{5}-\dfrac{7}{3}\right):\left(\dfrac{9}{20}-\dfrac{5}{12}+-3\right)\)
\(=\left(-\dfrac{27}{15}-\dfrac{36}{15}-\dfrac{21}{15}\right):\left(\dfrac{27}{60}-\dfrac{25}{60}+-3\right)\)
\(=\left(-\dfrac{28}{5}\right):\left(-\dfrac{89}{30}\right)\)
\(=\left(-\dfrac{28}{5}\right).\left(-\dfrac{30}{89}\right)\)
\(=\dfrac{168}{89}\)
19 tháng 7 2017
\(\dfrac{11.3^{22}.3^7-9^{15}}{\left(2.3^{14}\right)^2}\)
\(=\dfrac{11.3^{29}-\left(3^2\right)^{15}}{2^2.3^{28}}\)
\(=\dfrac{11.3^{29}-3^{30}}{2^2.3^{28}}\)
\(=\dfrac{3^{29}\left(11-3\right)}{2^2.3^{28}}\)
\(=\dfrac{3^{29}.2^3}{2^2.3^{28}}\)
\(=\dfrac{3.2}{1.1}=6\)
