\( \dfrac{{{a^2} + \sqrt a }}{{a - \sqrt a + 1}} - \dfrac{{2a + \sqrt a }}{{\sqrt a }} + 1\\ = \dfrac{{\sqrt a \left( {a\sqrt a + 1} \right)}}{{a - \sqrt a + 1}} - \dfrac{{\sqrt a \left( {2\sqrt a + 1} \right)}}{{\sqrt a }} + 1\\ = \dfrac{{\sqrt a \left( {\sqrt a + 1} \right)\left( {a - \sqrt a + 1} \right)}}{{a - \sqrt a + 1}} - \left( {2\sqrt a + 1} \right) + 1\\ = a + \sqrt a - 2\sqrt a - 1 + 1\\ = a - \sqrt a \)
\(\frac{a^2+\sqrt{a}}{a-\sqrt{a}+1}-\frac{2a+\sqrt{a}}{\sqrt{a}+1}=\frac{a^2\sqrt{a}+a+a^2+\sqrt{a}}{\left(a-\sqrt{a}+1\right)\left(\sqrt{a}+1\right)}-\frac{2a^2+a\sqrt{a}-2a\sqrt{a}-a+2a+\sqrt{a}}{\left(a-\sqrt{a}+1\right)\left(\sqrt{a}+1\right)}=\frac{\left(\sqrt{a}-\sqrt{a}\right)+\left(a+a-2a\right)+\left(a^2-2a^2\right)+\left(a^2\sqrt{a}+2a\sqrt{a}-a\sqrt{a}\right)}{\left(a-\sqrt{a}+1\right)\left(\sqrt{a}+1\right)}=\frac{a\left(a\sqrt{a}-\sqrt{a}-a\right)}{\left(a-\sqrt{a}+1\right)\left(\sqrt{a}+1\right)}=\frac{-a^2+a^2\sqrt{a}-a\sqrt{a}}{a^3-1}\)
\(dk:a>0;\frac{a^2+\sqrt{a}}{a-\sqrt{a}+1}-\frac{2a+\sqrt{a}}{\sqrt{a}}+1=\frac{a^2+\sqrt{a}}{a-\sqrt{a}+1}-2\sqrt{a}-1+1=\frac{a^2+\sqrt{a}}{a-\sqrt{a}+1}-2\sqrt{a}=\frac{a^2-a\sqrt{a}+a+\sqrt{a}-\sqrt{a}}{a-\sqrt{a}+1}-\sqrt{a}=\frac{a\left(a-\sqrt{a}+1\right)}{a-\sqrt{a}+1}-\sqrt{a}=a-\sqrt{a}\)
\(Taco:x-\sqrt{x}+\frac{1}{4}=\left(\sqrt{x}-\frac{1}{2}\right)^2\ge0\Rightarrow GTNNla:-\frac{1}{4}\Leftrightarrow x=\frac{1}{4}\)
