Bài 1:
\(=\dfrac{x-2+\sqrt{x}}{\sqrt{x}\left(\sqrt{x}+2\right)}\cdot\dfrac{\sqrt{x}+1}{\sqrt{x}-1}=\dfrac{\sqrt{x}+1}{\sqrt{x}}\)
Rút gọn A = \(\left(\frac{3}{\sqrt{x}-1}-\frac{\sqrt{x}-3}{x-1}\right)\div\left(\frac{x+2}{x+\sqrt{x}-2}-\frac{\sqrt{x}}{\sqrt{x}+2}\right)\)
Rút gọn : \(\left(\frac{\sqrt{x}}{\sqrt{x}-1}-\frac{1}{x-\sqrt{x}}\right):\left(\frac{1}{x+\sqrt{x}}-\frac{2}{1-x}\right)\)
a) Cho \(x,y,z\ne0\) và \(x-y-z=0\) . Tính \(K=\left(1-\frac{z}{x}\right)\left(1-\frac{x}{y}\right)\left(1+\frac{y}{z}\right)\)
b) \(\frac{3x-2y}{4}=\frac{2z-4x}{3}=\frac{4y-3z}{2}\) Chứng minh \(\frac{x}{2}=\frac{y}{3}=\frac{z}{4}\)
Rút gọn : \(\left(\frac{\sqrt{x}-1}{\sqrt{x+1}}+\frac{\sqrt{x}+1}{\sqrt{x-1}}\right).\left(1-\frac{2}{x+1}\right)^2\)
\(A=\left[\frac{\sqrt{x}}{\sqrt{x}-3}-\frac{3\sqrt{x}+9}{x-9}+\frac{2\sqrt{x}}{\sqrt{x}+3}\right]\div\left[\frac{2\sqrt{x}-2}{\sqrt{x}-3}-1\right]\)
a) Tìm tập xác định và rút gọn A
b) \(x=?\) để \(A< -1\)
Rút gọn D = \(\left(\frac{\sqrt{x}+\sqrt{y}}{2\sqrt{x}-2\sqrt{y}}-\frac{2\sqrt{x}}{x-y}\right).\frac{2\sqrt{x}}{\sqrt{x}-\sqrt{y}}\)
Rút gọn: \(\left(\frac{x-y}{2y-x}-\frac{x^2+y^2+y-2}{x^2-xy-2y^2}\right):\frac{4x^4+4x^2y+y^2-4}{x^2+xy+x+y}:\frac{x+1}{2y^2+y+2}\)
cho 3 số dương x,y,z thỏa mãn : \(x+y+z=xyz\)
CMR : \(\frac{x}{1+x^2}+\frac{2y}{1+y^2}+\frac{3z}{1+z^2}=\frac{xyz\left(5x+4y+3z\right)}{\left(x+y\right)\left(y+z\right)\left(z+x\right)}\)
Rút gọn:
\(\left(\frac{1}{x^2-xy}-\frac{3y^2}{x^4-xy^3}-\frac{y}{x^3+x^2y}\right).\left(y+\frac{x^2}{x+y}\right)\)
