Ta có: \(P=\left(\dfrac{3x-6\sqrt{x}}{x\sqrt{x}-2x}-\dfrac{1}{2-\sqrt{x}}+\dfrac{\sqrt{x}-3}{\sqrt{x}}\right)\cdot\left(1-\dfrac{\sqrt{x}-3}{\sqrt{x}-2}\right)\)

\(=\left(\dfrac{3\sqrt{x}\left(\sqrt{x}-2\right)}{x\left(\sqrt{x}-2\right)}+\dfrac{1}{\sqrt{x}-2}+\dfrac{\sqrt{x}-3}{\sqrt{x}}\right)\cdot\left(\dfrac{\sqrt{x}-2}{\sqrt{x}-2}-\dfrac{\sqrt{x}-3}{\sqrt{x}-2}\right)\)

\(=\left(\dfrac{3\left(\sqrt{x}-2\right)}{\sqrt{x}\left(\sqrt{x}-2\right)}+\dfrac{\sqrt{x}}{\sqrt{x}\left(\sqrt{x}-2\right)}+\dfrac{\left(\sqrt{x}-3\right)\left(\sqrt{x}-2\right)}{\sqrt{x}\left(\sqrt{x}-2\right)}\right)\cdot\dfrac{\sqrt{x}-2-\sqrt{x}+3}{\sqrt{x}-2}\)\(=\dfrac{3\sqrt{x}-6+\sqrt{x}+x-5\sqrt{x}+6}{\sqrt{x}\left(\sqrt{x}-2\right)}\cdot\dfrac{1}{\sqrt{x}-2}\)

\(=\dfrac{x-\sqrt{x}}{\sqrt{x}\left(\sqrt{x}-2\right)}\cdot\dfrac{1}{\sqrt{x}-2}\)

\(=\dfrac{\sqrt{x}\left(\sqrt{x}-1\right)}{\sqrt{x}\left(\sqrt{x}-2\right)}\cdot\dfrac{1}{\sqrt{x}-2}\)

\(=\dfrac{\sqrt{x}-1}{\left(\sqrt{x}-2\right)^2}\)

`P= 8x^3 -4x^2 +2x+1+x^3+x^2-x+1`

`P=9x^3 -3x^2+x+2`

\(\text{ P = (2x-1).4x^2+2x+1+(x+1)x^2-x+1}\)

\(\text{P =}\) \(\text{[(2x-1) . 4x^2 ]}\)\(\text{[(x+1) .x^2]}\)

\(\text{P = }\) \(\text{8x^3 - 4x^2 + 2x^3 + 2x^2 + 2x + 1 + x^3 - x + 1}\)

\(\text{P =}\) \(\text{(8x^3 + 2x^3 + x^3) + (-4x^2 + 2x^2) + (2x - x) + (1 + 1)}\)

\(\text{P =}\) \(\text{11x^3 - 2x^2 + x + 2}\)

ĐKXĐ: \(x\ge0;x\ne4\)

\(P=\dfrac{x+\sqrt{x}}{\sqrt{x}-2}-\dfrac{2\sqrt{x}-1}{\sqrt{x}+2}+\dfrac{x-6\sqrt{x}+4}{x-4}\)

\(=\dfrac{\left(x+\sqrt{x}\right)\left(\sqrt{x}+2\right)-\left(2\sqrt{x}-1\right)\left(\sqrt{x}-2\right)+x-6\sqrt{x}+4}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)

\(=\dfrac{x\sqrt{x}+2x+x+2\sqrt{x}-\left(2x-4\sqrt{x}-\sqrt{x}+2\right)+x-6\sqrt{x}+4}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)

\(=\dfrac{x\sqrt{x}+2x+x+2\sqrt{x}-2x+4\sqrt{x}+\sqrt{x}-2+x-6\sqrt{x}+4}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)

\(=\dfrac{x\sqrt{x}+2x+\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)

\(=\dfrac{\sqrt{x}\left(x+1\right)+2\left(x+1\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)

\(=\dfrac{\left(x+1\right)\left(\sqrt{x}+2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}=\dfrac{x+1}{\sqrt{x}-2}\)

Khi \(x=9+4\sqrt{5}\)

Ta có: \(4+4\sqrt{5}+5=2^2+2\cdot2\cdot\sqrt{5}+\left(\sqrt{5}\right)^2=\left(2+\sqrt{5}\right)^2\)

\(\Rightarrow\sqrt{x}=2+\sqrt{5}\)

\(\Rightarrow P=\dfrac{\left(2+\sqrt{5}\right)^2+1}{2+\sqrt{5}-2}=\dfrac{9+4\sqrt{5}+1}{\sqrt{5}}=\dfrac{10+4\sqrt{5}}{\sqrt{5}}=4+2\sqrt{5}\)

Vậy \(P=4+2\sqrt{5}\) khi \(x=9+4\sqrt{5}\).

\(D=\dfrac{x\sqrt{x}+2x+x+2\sqrt{x}-2x+4\sqrt{x}+\sqrt{x}-2+x-6\sqrt{x}+4}{x-4}\)

\(=\dfrac{x\sqrt{x}+2x+2}{x-4}\)

Khi x=9+4căn 5 thì \(D=\dfrac{\left(9+4\sqrt{5}\right)\left(\sqrt{5}+2\right)+2\sqrt{5}+4+2}{\sqrt{5}-2}\)

\(=\dfrac{9\sqrt{5}+18+20+8\sqrt{5}+2\sqrt{5}+6}{\sqrt{5}-2}\)

=(44+19căn 5)*(căn 5+2)

=44căn 5+88+95+38căn 5

=82căn 5+183

P = \(\dfrac{\sqrt{x}\left(\sqrt{x}+1\right)}{\sqrt{x}+1}+\dfrac{\sqrt{x}\left(\sqrt{x}-1\right)}{\sqrt{x}-1}\)DKXD: \(\left\{{}\begin{matrix}x\ge0\\x\ne1\end{matrix}\right.\)

   = \(\sqrt{x}+\sqrt{x}\)

   = \(2\sqrt{x}\)

Vậy tại x ∈ ĐKXĐ thì P = \(2\sqrt{x}\)

Ta có: \(P=\dfrac{\sqrt{x}\left(\sqrt{x}+1\right)}{\sqrt{x}+1}+\dfrac{\sqrt{x}\left(\sqrt{x}-1\right)}{\sqrt{x}-1}\)

\(=\sqrt{x}+\sqrt{x}\)

\(=2\sqrt{x}\)

\(P=\left(\dfrac{x}{x-\sqrt{x}}+\dfrac{1}{\sqrt{x}+1}-\dfrac{2}{1-x}\right):\left(\dfrac{\sqrt{x}-2}{1-\sqrt{x}}\right)\)

\(P=\left(\dfrac{\sqrt{x}\left(\sqrt{x}+1\right)}{\left(x-1\right)}+\dfrac{\left(\sqrt{x}-1\right)}{\left(x-1\right)}+\dfrac{2}{x-1}\right):\left(\dfrac{\sqrt{x}-2}{1-\sqrt{x}}\right)\)

\(P=\dfrac{x+\sqrt{x}+\sqrt{x}-1+2}{x-1}:\dfrac{\sqrt{x}-2}{1-\sqrt{x}}=\dfrac{x+2\sqrt{x}+1}{x-1}:\dfrac{\sqrt{x}-2}{1-\sqrt{x}}\)

\(P=\dfrac{\left(\sqrt{x}+1\right)^2}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}:\dfrac{\sqrt{x}-2}{1-\sqrt{x}}=-\dfrac{\sqrt{x}+1}{\sqrt{x}-2}\)

P=x^3+3/5x^2y-3xy-3/5x^2y-xy+x^3

=2x^3-4xy

=2*(-2)^3-4*(-2)*1/3

=-16+8/3=-40/3

Ta có: \(P=\left(\dfrac{x-2\sqrt{x}+3}{x-2\sqrt{x}-3}-\dfrac{x}{x-3\sqrt{x}}\right):\dfrac{1-\sqrt{x}}{3-\sqrt{x}}\)

\(=\left(\dfrac{x\sqrt{x}-2x+3\sqrt{x}}{\sqrt{x}\left(\sqrt{x}-3\right)\left(\sqrt{x}+1\right)}-\dfrac{x\left(\sqrt{x}+1\right)}{\sqrt{x}\left(\sqrt{x}-3\right)\left(\sqrt{x}+1\right)}\right):\dfrac{\sqrt{x}-1}{\sqrt{x}-3}\)

\(=\dfrac{x\sqrt{x}-2x+3\sqrt{x}-x\sqrt{x}-x}{\sqrt{x}\left(\sqrt{x}-3\right)\left(\sqrt{x}+1\right)}\cdot\dfrac{\sqrt{x}-3}{\sqrt{x}-1}\)

\(=\dfrac{-3x+3\sqrt{x}}{\sqrt{x}\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\)

\(=\dfrac{-3\sqrt{x}\left(\sqrt{x}-1\right)}{\sqrt{x}\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\)

\(=\dfrac{-3}{\sqrt{x}+1}\)

\(P=\left(\dfrac{2\sqrt{x}+2}{x\sqrt{x}-\sqrt{x}+x-1}-\dfrac{1}{\sqrt{x}-1}\right):\left(1+\dfrac{1}{\sqrt{x}+1}\right)\)

\(P=\left(\dfrac{2}{\left(x-1\right)}-\dfrac{1}{\sqrt{x}-1}\right):\left(\dfrac{\sqrt{x}+2}{\sqrt{x}+1}\right)\)

\(P=\left(\dfrac{2}{\left(x-1\right)}-\dfrac{\left(\sqrt{x}+1\right)}{\left(x-1\right)}\right):\left(\dfrac{\sqrt{x}+2}{\sqrt{x}+1}\right)\)

\(P=\left(\dfrac{1-\sqrt{x}}{x-1}\right):\left(\dfrac{\sqrt{x}+2}{\sqrt{x}+1}\right)=-\left(\sqrt{x}+2\right)\)

ĐKXĐ x\(\ge0;x\ne1\)

Ta có: \(P=\left(\dfrac{2\sqrt{x}+x+1}{\sqrt{x}+1}\right)\cdot\left(1-\dfrac{x-\sqrt{x}}{\sqrt{x}-1}\right):\left(1-\sqrt{x}\right)\)

\(=\left(\dfrac{\left(\sqrt{x}+1\right)^2}{\sqrt{x}+1}\right)\cdot\left(1-\dfrac{\sqrt{x}\left(\sqrt{x}-1\right)}{\sqrt{x}-1}\right)\cdot\dfrac{1}{1-\sqrt{x}}\)

\(=\left(\sqrt{x}+1\right)\left(1-\sqrt{x}\right)\cdot\dfrac{1}{1-\sqrt{x}}\)

\(=\sqrt{x}+1\)