rút gọn
2,5 xy (0,1x2 - 0,4xy2)
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Theo đề =>\(0,1F=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99,100}\)
\(\Rightarrow0,1F=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)
\(\Rightarrow0,1F=1-\frac{1}{100}=\frac{99}{100}\)
\(\Rightarrow F=\frac{99}{10}\)
Chúc bạn hc tốt :)
\(0,1x^2-0,6x-0,8=0\\ \Leftrightarrow x^2-6x-8=0\\ \Leftrightarrow\left\{{}\begin{matrix}x_1+x_2=6\\x_1.x_2=-8\end{matrix}\right.\)
\(\dfrac{\sqrt{y}}{\sqrt{xy}-x}-\dfrac{\sqrt{x}}{y-\sqrt{xy}}\)
\(=\dfrac{\sqrt{y}}{\sqrt{x}\left(\sqrt{y}-\sqrt{x}\right)}-\dfrac{\sqrt{x}}{\sqrt{y}\left(\sqrt{y}-\sqrt{x}\right)}\)
\(=\dfrac{y-x}{\sqrt{xy}\left(\sqrt{y}-\sqrt{x}\right)}=\dfrac{\sqrt{y}+\sqrt{x}}{\sqrt{xy}}\)
\(\frac{xy+2x-y-2}{xy-x-y+1}=\frac{\left(xy-y\right)+\left(2x-2\right)}{\left(xy-y\right)+\left(1-x\right)}\)
\(=\frac{\left(x-1\right)\left(y+2\right)}{\left(x-1\right)\left(y-1\right)}=\frac{y+2}{y-1}\)
\(\frac{\left(xy-y\right)+\left(2x-2\right)}{\left(xy-y\right)-\left(x-1\right)}=\frac{y\left(x-1\right)+2\left(x-1\right)}{y\left(x-1\right)-\left(x-1\right)}=\frac{\left(x-1\right)\left(y+2\right)}{\left(x-1\right)\left(y-1\right)}=\frac{y+2}{y-1}\)
\(A=x^2\left(x-y^2\right)-xy\left(1-xy\right)-x^3\\ =x^3-x^2y^2-xy+x^2y^2-x^3\\ =\left(x^3-x^3\right)+\left(-x^2y^2+x^2y^2\right)-xy\\ =-xy\)
Điều kiện \(x\ne\pm3;y\ne-2\):
\(P=\frac{2x+3y}{xy+2x-3y-6}-\frac{6-xy}{xy+2x+3y+6}-\frac{x^2+9}{x^2-9}.\)
=> \(P=\frac{2x+3y}{\left(y+2\right)\left(x-3\right)}-\frac{6-xy}{\left(y+2\right)\left(x+3\right)}-\frac{x^2+9}{\left(x-3\right)\left(x+3\right)}\)
\(P=\frac{\left(2x+3y\right)\left(x+3\right)-\left(6-xy\right)\left(x-3\right)-\left(x^2+9\right)\left(y+2\right)}{\left(y+2\right)\left(x-3\right)\left(x+3\right)}\)
\(P=\frac{2x^2+3xy+6x+9y-6x+x^2y+18-3xy-x^2y-9y-2x^2-18}{\left(y+2\right)\left(x-3\right)\left(x+3\right)}\)
\(P=\frac{0}{\left(y+2\right)\left(x-3\right)\left(x+3\right)}=0\)
=> P=0 (với mọi x khác 3, -3 và y khác -2)