Question

[bùi diệu anh]

rút gọn A=\(\dfrac{2a\sqrt{a}+2\sqrt{a}-3a-3}{2\sqrt{a}-3}\)

B =\(\dfrac{2a^2-2a}{\sqrt{a^3}-\sqrt{a}}\)

rồi so sánh

Answer 1

[Nguyễn Lê Phước Thịnh]

\(A=\dfrac{2\sqrt{a}\left(a+1\right)-3\left(a+1\right)}{2\sqrt{a}-3}=a+1\)

\(B=\dfrac{2a\left(a-1\right)}{\sqrt{a}\left(a-1\right)}=2\sqrt{a}\)

\(A-B=a+1-2\sqrt{a}=\left(\sqrt{a}-1\right)^2>=0\)

=>A>=B