a: \(A=\dfrac{2u+\sqrt{uv}-3v}{2u-5\sqrt{uv}+3v}\)
\(=\dfrac{2u-2\sqrt{uv}+3\sqrt{uv}-3v}{2u-2\sqrt{uv}-3\sqrt{uv}+3v}\)
\(=\dfrac{2\sqrt{u}\left(\sqrt{u}-\sqrt{v}\right)+3\sqrt{v}\left(\sqrt{u}-\sqrt{v}\right)}{2\sqrt{u}\left(\sqrt{u}-\sqrt{v}\right)-3\sqrt{v}\left(\sqrt{u}-\sqrt{v}\right)}\)
\(=\dfrac{\left(\sqrt{u}-\sqrt{v}\right)\left(2\sqrt{u}+3\sqrt{v}\right)}{\left(\sqrt{u}-\sqrt{v}\right)\left(2\sqrt{u}-3\sqrt{v}\right)}=\dfrac{2\sqrt{u}+3\sqrt{v}}{2\sqrt{u}-3\sqrt{v}}\)
b: \(B=\dfrac{x+\sqrt{5}}{x^2+2x\sqrt{5}+5}\)
\(=\dfrac{x+\sqrt{5}}{\left(x+\sqrt{5}\right)^2}=\dfrac{1}{x+\sqrt{5}}\)
c: \(C=0,2x^3y^3\cdot\sqrt{\dfrac{16}{x^4y^8}}\)
\(=0,2x^3y^3\cdot\dfrac{4}{x^2y^4}\)
\(=4\cdot0,2\cdot\dfrac{x^3y^3}{x^2y^4}=0,8\cdot\dfrac{x}{y}\)
d: \(D=\dfrac{x-1}{\sqrt{y}-1}\cdot\sqrt{\dfrac{\left(y-2\sqrt{y}+1\right)^2}{\left(x-1\right)^4}}\)
\(=\dfrac{x-1}{\sqrt{y}-1}\cdot\dfrac{\left|y-2\sqrt{y}+1\right|}{\left(x-1\right)^2}\)
\(=\dfrac{x-1}{\left(x-1\right)^2}\cdot\dfrac{\left(\sqrt{y}-1\right)^2}{\sqrt{y}-1}=\dfrac{\sqrt{y}-1}{x-1}\)
