Question

Rút gọn bthuc ( ko dùng mt cầm tay)

\(\dfrac{a+b-2\sqrt{ab}}{\left(\sqrt{a}-\sqrt{b}\right)}\):\(\dfrac{1}{\sqrt{a}+\sqrt{b}}\)     ( a>0, b>0, a khác b).

Answer 1

\(A=\dfrac{\left(\sqrt{a}-\sqrt{b}\right)^2}{\left(\sqrt{a}-\sqrt{b}\right)}\cdot\left(\sqrt{a}+\sqrt{b}\right)\)

\(=\left(\sqrt{a}-\sqrt{b}\right)\left(\sqrt{a}+\sqrt{b}\right)\)

=a-b

Answer 2

Với `a > 0,b > 0,a \ne b` có:

   `[a+b-2\sqrt{ab}]/[\sqrt{a}-\sqrt{b}]:1/[\sqrt{a}+\sqrt{b}]`

`=[(\sqrt{a}-\sqrt{b})^2]/[\sqrt{a}-\sqrt{b}]. (\sqrt{a}+\sqrt{b})`

`=(\sqrt{a}-\sqrt{b})(\sqrt{a}+\sqrt{b})`

`=a-b`

Answer 3

\(=\dfrac{\left(\sqrt{a}-\sqrt{b}^2\right)}{\left(\sqrt{a-\sqrt{b}}\right)}:\left(\sqrt{a+\sqrt{b}}\right)\)

\(=\left(\sqrt{a-\sqrt{b}}\right).\left(\sqrt{a+\sqrt{b}}\right)\)

ĐA:\(a-b\)