Question

Rút gọn các biểu thức (giả thiết các biểu thức chữ đều có nghĩa

\(1,A=\dfrac{\sqrt{15}-\sqrt{5}}{\sqrt{3}-1}\)         \(B.=\dfrac{a+\sqrt{ab}}{\sqrt{a}+\sqrt{b}}\)     \(C,=\left(\dfrac{1}{\sqrt{a-1}}+\dfrac{1}{\sqrt{a}\left(\sqrt{a-1}\right)}\right)\left(\dfrac{a-2\sqrt{a+1}}{\sqrt{a}+1}\right)\)                

Answer 1

`A=[\sqrt{15}-\sqrt{5}]/[\sqrt{3}-1]=[\sqrt{5}(\sqrt{3}-1)]/[\sqrt{3}-1]=\sqrt{5}`

`B=[a+\sqrt{ab}]/[\sqrt{a}+\sqrt{b}]=[\sqrt{a}(\sqrt{a}+\sqrt{b})]/[\sqrt{a}+\sqrt{b}]=\sqrt{a}`

`C=(1/\sqrt{a-1}+1/[\sqrt{a}\sqrt{a-1}])([a-2\sqrt{a+1}]/[\sqrt{a}+1]`

`C=[\sqrt{a}+1]/[\sqrt{a}\sqrt{a-1}].[a-2\sqrt{a+1}]/[\sqrt{a}+1]`

`C=[a-2\sqrt{a+1}]/[\sqrt{a}\sqrt{a-1}]`

Answer 2

`a, A = (sqrt 5(sqrt 3 - sqrt 1))/(sqrt 3 - 1) = sqrt 5`

`b, B = (a + sqrt (ab))/(sqrt a + sqrt b) = (sqrt a(sqrt a + sqrt b))/(sqrt a +sqrtb)`

`= sqrt a`

`c, C = (sqrt a + 1)/(sqrt a(sqrt a - 1)) . (sqrt a-1)^2/(sqrt a . sqrt (a-1))`

`= (sqrt a + 1)/(a)`.