a/ A = \(\dfrac{a^2+\sqrt{a}}{a-\sqrt{a}+1}-\dfrac{2a+\sqrt{a}}{\sqrt{a}}+1\) ( ĐKXĐ : a >0 )
= \(\dfrac{\sqrt{a}\left(a\sqrt{a}+1\right)}{a-\sqrt{a}+1}-\dfrac{\sqrt{a}\left(2\sqrt{a}+1\right)}{\sqrt{a}}+1\)
= \(\dfrac{\sqrt{a}\left(\sqrt{a}+1\right)\left(a-\sqrt{a}+1\right)}{a-\sqrt{a}+1}-\dfrac{\sqrt{a}\left(2\sqrt{a}+1\right)}{\sqrt{a}}+1\)
= \(\sqrt{a}\left(\sqrt{a}+1\right)-\left(2\sqrt{a}+1\right)+1\)
= \(a+\sqrt{a}-2\sqrt{a}-1+1\)
= \(a-\sqrt{a}\) = \(\sqrt{a}\left(\sqrt{a}-1\right)\)
vậy biểu thức sau khi đã được rút gọn có kết quả là \(\sqrt{a}\left(\sqrt{a}-1\right)\)
b/ Min A= 0 \(\Leftrightarrow\sqrt{a}-1=0\)
\(\Leftrightarrow\sqrt{a}=1\)
\(\Leftrightarrow a=1\)