Rút gọn:
\(B=\dfrac{x-2}{x+2}\cdot\left(\dfrac{5x+10}{7x-14}+\dfrac{x-2}{3x-6}\right)+\dfrac{3\cdot\left(x^2-4\right)}{2x^2-8x+8}\)
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PT
11 tháng 7 2017
\(D=\dfrac{x-2}{x+2}.\left(\dfrac{5x+10}{7x-14}+\dfrac{x-2}{3x-6}\right)+\dfrac{3x^2-12}{2x^2-8x+8}\)
\(D=\dfrac{x-2}{x+2}.\left(\dfrac{5\left(x+2\right)}{7\left(x-2\right)}+\dfrac{x-2}{3\left(x-2\right)}\right)+\dfrac{3\left(x^2-4\right)}{2\left(x^2-4x+4\right)}\)
\(D=\dfrac{x-2}{x+2}.\dfrac{5\left(x+2\right)}{7\left(x-2\right)}+\dfrac{x-2}{3\left(x-2\right)}.\dfrac{x-2}{x+2}+\dfrac{3\left(x^2-4\right)}{2\left(x^2-4x+4\right)}\)
\(D=\dfrac{5}{7}+\dfrac{x-2}{2\left(x+2\right)}+\dfrac{3\left(x-2\right)\left(x+2\right)}{2\left(x-2\right)^2}\)
\(D=\dfrac{5}{7}+\dfrac{x-2}{2\left(x+2\right)}+\dfrac{3\left(x+2\right)}{2\left(x-2\right)}\)
\(D=\dfrac{5}{7}-\dfrac{-\left(x-2\right)}{2\left(x-2\right)}+\dfrac{3\left(x+2\right)}{2\left(x-2\right)}\)
\(D=\dfrac{5}{7}-\dfrac{-\left(x-2\right)+3x+2}{2\left(x-2\right)}\)
\(D=\dfrac{5}{7}-\dfrac{2x+4}{2\left(x-2\right)}\)
\(D=\dfrac{5}{7}+\dfrac{2\left(x-2\right)}{2\left(x-2\right)}=\dfrac{5}{7}+\dfrac{x-2}{x-2}\)
\(D=\dfrac{5}{7}+1=\dfrac{12}{7}\)
Vậy \(D=\dfrac{12}{7}\)
9 tháng 5 2023
a: \(P=\left(\dfrac{3x+6}{2\left(x^2+4\right)}-\dfrac{2x^2-x-10}{\left(x+1\right)\left(x^2+1\right)}\right):\left(\dfrac{10\left(x^2-1\right)+3\left(x^2+1\right)\left(x-1\right)-6\left(x+1\right)\left(x^2+1\right)}{\left(x^2+1\right)\left(x+1\right)\left(x-1\right)\cdot2}\right)\cdot\dfrac{2}{x-1}\)
\(=\left(\dfrac{\left(3x+6\right)\left(x^3+x^2+x+1\right)-\left(2x^2+8\right)\left(2x^2-x-10\right)}{2\left(x^2+4\right)\left(x+1\right)\left(x^2+1\right)}\right)\cdot\dfrac{\left(x^2+1\right)\left(x-1\right)\left(x+1\right)\cdot2}{-3x^3+x^2-3x-13}\cdot\dfrac{2}{x-1}\)
\(=\dfrac{-x^4+11x^3+13x^2+17x+16}{\left(x^2+4\right)}\cdot\dfrac{2}{-3x^3+x^2-3x-13}\)
19 tháng 7 2017
\(\dfrac{11.3^{22}.3^7-9^{15}}{\left(2.3^{14}\right)^2}\)
\(=\dfrac{11.3^{29}-\left(3^2\right)^{15}}{2^2.3^{28}}\)
\(=\dfrac{11.3^{29}-3^{30}}{2^2.3^{28}}\)
\(=\dfrac{3^{29}\left(11-3\right)}{2^2.3^{28}}\)
\(=\dfrac{3^{29}.2^3}{2^2.3^{28}}\)
\(=\dfrac{3.2}{1.1}=6\)
8 tháng 7 2017
\(a,2\left(5x+1\right)-7\left(3x-2\right)=4\left(2x-1\right)+3\left(2-x\right)\)
\(\Leftrightarrow10x+2-21x+14=8x-4+6-3x\)
\(\Leftrightarrow-16x=-14\)
\(\Rightarrow x=\dfrac{7}{8}\)
\(b,-4\left(\dfrac{1}{2}x-3\right)+\dfrac{7}{2}\left(2x-1\right)+x=5x\left(1-x\right)\)
\(\Leftrightarrow-2x+12+7x-\dfrac{7}{2}+x=5x-5x^2\)
\(\Leftrightarrow5x^2+x+\dfrac{17}{2}=0\)
Cái này không biết tách kiểu gì cho vừa nên bạn nhấn máy tính nhé
Mode 5 3 rồi lần lượt điền vào theo thứ tự trên thì
\(\Rightarrow\left[{}\begin{matrix}x=-\dfrac{1}{10}+\dfrac{13i}{10}\\x=-\dfrac{1}{10}-\dfrac{13i}{10}\end{matrix}\right.\)
PN
13 tháng 7 2017
Bài 1:
\(\left(-\dfrac{72}{40}-\dfrac{144}{60}-2\dfrac{1}{3}\right):\left(\dfrac{45}{100}-\dfrac{25}{60}+-\dfrac{75}{25}\right)\)
\(=\left(-\dfrac{9}{5}-\dfrac{12}{5}-\dfrac{7}{3}\right):\left(\dfrac{9}{20}-\dfrac{5}{12}+-3\right)\)
\(=\left(-\dfrac{27}{15}-\dfrac{36}{15}-\dfrac{21}{15}\right):\left(\dfrac{27}{60}-\dfrac{25}{60}+-3\right)\)
\(=\left(-\dfrac{28}{5}\right):\left(-\dfrac{89}{30}\right)\)
\(=\left(-\dfrac{28}{5}\right).\left(-\dfrac{30}{89}\right)\)
\(=\dfrac{168}{89}\)
\(B=\dfrac{x-2}{x+2}\cdot\left(\dfrac{5x+10}{7x-14}+\dfrac{x-2}{3x-6}\right)+\dfrac{3\left(x^2-4\right)}{2x^2-8x+8}\)
\(=\dfrac{x-2}{x+2}\cdot\left(\dfrac{5x+10}{7\left(x-2\right)}+\dfrac{x-2}{3\left(x-2\right)}\right)+\dfrac{3\left(x-2\right)\left(x+2\right)}{2\left(x^2-4x+4\right)}\)
\(=\dfrac{x-2}{x+2}\cdot\left(\dfrac{5x+10}{7\left(x-2\right)}+\dfrac{1}{3}\right)+\dfrac{3\left(x-2\right)\left(x+2\right)}{2\left(x-2\right)^2}\)
\(=\dfrac{x-2}{x+2}\cdot\dfrac{3\left(5x+10\right)+7\left(x-2\right)}{21\left(x-2\right)}+\dfrac{3\left(x+2\right)}{2\left(x-2\right)}\)
\(=\dfrac{1}{x+2}\cdot\dfrac{15x+30+7x-14}{21}+\dfrac{3x+6}{2\left(x-2\right)}\)
\(=\dfrac{22x+16}{21\left(x+2\right)}+\dfrac{3x+6}{2\left(x-2\right)}\)
\(=\dfrac{2\left(x-2\right)\left(22x+16\right)+21\left(x+2\right)\left(3x+6\right)}{42\left(x+2\right)\left(x-2\right)}\)
\(=\dfrac{\left(2x-4\right)\left(22x+16\right)+\left(21x+42\right)\left(3x+6\right)}{42\left(x^2-4\right)}\)
\(=\dfrac{44x^2+32x-88x-64+63x^2+126x+126x+252}{42x^2-168}\)
\(=\dfrac{107x^2+196x+188}{42x^2-168}\)