\(=\dfrac{x}{x-3}-\dfrac{x\left(x+3\right)}{2x+3}\cdot\left(\dfrac{x+3}{x\left(x-3\right)}-\dfrac{x}{\left(x+3\right)\left(x-3\right)}\right)\)
\(=\dfrac{x}{x-3}-\dfrac{x\left(x+3\right)}{2x+3}\cdot\dfrac{x^2+6x+9-x^2}{x\left(x-3\right)\left(x+3\right)}\)
\(=\dfrac{x}{x-3}-\dfrac{6x+9}{2x+3}\cdot\dfrac{1}{x-3}\)
\(=\dfrac{x-3}{x-3}=1\)
Rút gọn : \(\left[\left(x^3-1-\frac{7-x^3}{3+x^3}\right).\frac{4}{x^5+3x^2}\right]:\left[\frac{3x^6-12}{x^9+6x^6+9x^3}.\frac{x}{3x^3+6}\right]\)
Rút gọn A : \(\left[\frac{\left(x-1\right)^2}{3x+\left(x-1\right)^2}-\frac{1-2x^2+4x}{x^3-1}+\frac{1}{x-1}\right]:\frac{2x}{x^3+x}\)
Rút gọn : \(\frac{x^2+2x-3}{x^2+3x-10}:\frac{x^2+x-6}{x^2-9x+14}:\frac{x^2-4x+3}{x^2+7x+10}\)
1) Rút gọn : \(\left(\frac{x-2}{x+2\sqrt{x}}+\frac{1}{\sqrt{x}+2}\right):\frac{\sqrt{x}-1}{\sqrt{x}+1}\)
2) CHo \(\frac{3x-2y}{4}=\frac{2z-4x}{3}=\frac{4y-3z}{2}\). CMR \(\frac{x}{2}=\frac{y}{3}=\frac{z}{4}\)
Rút gọn A = \(\left[\left(1+\frac{1}{x^2}\right)\div\left(1+2x+x^2\right)+\frac{2}{\left(x+1\right)^3}\left(1+\frac{1}{x}\right)\right]\div\frac{x-1}{x^3}\)
Tìm tập xác định
Rút gon: \(\left(\frac{x^2+3x}{x^3+3x^2+9x+27}\right):\left(\frac{1}{x-3}-\frac{6x}{x^3-3x^2+9x-27}\right)\)
Rút gọn : \(\frac{2+x}{2-x}\div\frac{4x^2}{4-4x+x^2}.\left(\frac{2}{2-x}-\frac{8}{8+x^3}.\frac{4-2x+x^2}{2-x}\right)\)
Tìm tập xác định
Rút gọn : \(\frac{1}{\left(x+y\right)^3}.\left(\frac{1}{x^3}+\frac{1}{y^3}\right)+\frac{3}{\left(x+y\right)^5}\left(\frac{1}{x^2}+\frac{1}{y^2}\right)+\frac{6}{\left(x+y\right)^5}\left(\frac{1}{x}+\frac{1}{y}\right)\)
