Question

[Ngọc Huyền]

Cho biểu thức: B= \(\left(\frac{1}{a-\:\sqrt{a}}+\frac{1}{\sqrt{a-1}}\right):\frac{\sqrt{a}+1}{A-2\sqrt{a}+1}\)

a, Rút gọn B

b, So sánh B với 1

Answer 1

[Hoàng Lê Bảo Ngọc]

ĐKXĐ : \(a>0,a\ne1\)

a) \(\left(\frac{1}{a-\sqrt{a}}+\frac{1}{\sqrt{a}-1}\right):\frac{\sqrt{a}+1}{a-2\sqrt{a}+1}=\frac{1+\sqrt{a}}{\sqrt{a}\left(\sqrt{a}-1\right)}:\frac{\sqrt{a}+1}{\left(\sqrt{a}-1\right)^2}=\frac{\sqrt{a}+1}{\sqrt{a}\left(\sqrt{a}-1\right)}.\frac{\left(\sqrt{a}-1\right)^2}{\sqrt{a}+1}=\frac{\sqrt{a}-1}{\sqrt{a}}\)

b) \(B=1-\frac{1}{\sqrt{a}}< 1\)

Answer 2

[Ngọc Huyền]

Cảm ơn ạ!