Question

Cho biểu thức:

A = \(\dfrac{\sqrt{a}+1}{\sqrt{a}-3}\)           B = \(\dfrac{2\sqrt{a}}{\sqrt{a}+3}-\dfrac{\sqrt{a}}{3-\sqrt{a}}-\dfrac{3a+3}{a-9}\) (với a ≥ 0; a ≠ 9)

a) Tính giá trị của A khi a = 16.

b) Rút gọn biểu thức P = \(\dfrac{A}{B}\)

c) So sánh P với 1

Answer 1

a: Khi a=16 thì \(A=\dfrac{4+1}{4-3}=5\)

b: \(P=\dfrac{\sqrt{a}+1}{\sqrt{a}-3}:\dfrac{2a-6\sqrt{a}+a+3\sqrt{a}-3a-3}{a-9}\)

\(=\dfrac{\sqrt{a}+1}{\sqrt{a}-3}:\dfrac{-3\left(\sqrt{a}+1\right)}{a-9}=\dfrac{-\sqrt{a}-3}{3}\)

Answer 2

`(a):\  a=16(TMDK)=>A=(\sqrt{16}+1)/(\sqrt{16}-3)=(4+1)/(4-3)=5`

`(b):\ B=(2\sqrt{a})/(\sqrt{a}+3)+(\sqrt{a})/(\sqrt{a}-3)-(3a+3)/((\sqrt{a}-3)(\sqrt{a}+3))\    (a\ge0;a\ne 9)`

`=(2\sqrt{a}(\sqrt{a}-3)+\sqrt{a}(\sqrt{a}+3)-(3a+3))/((\sqrt{a}-3)(\sqrt{a}+3))`

`=(2a-6\sqrt{a}+a+3\sqrt{a}-3a-3)/((\sqrt{a}-3)(\sqrt{a}+3))`

`=(-3\sqrt{a}-3)/((\sqrt{a}-3)(\sqrt{a}+3))`

``

`P=A/B\  (ĐK:x\ge 0;x\ne 9)`

`=(\sqrt{a}+1)/(\sqrt{a}-3):(-3(\sqrt{a}+1))/((\sqrt{a}-3)(\sqrt{a}+3))`

`=(\sqrt{a}+1)/(\sqrt{a}-3).((\sqrt{a}-3)(\sqrt{a}+3))/(-3(\sqrt{a}+1))`

`=-(\sqrt{a}+3)/(3)`

`(c):\  P-1=-(\sqrt{a}+3)/(3)-1=(-\sqrt{a}-3-3)/(3)`

`=(-\sqrt{a}-6)/(3)=-(\sqrt{a}+6)/(3)`

Vì : `\sqrt{a}+6 \ge 6>0` với mọi `x\in ĐK`

`=>(\sqrt{a}+6)/(3) >0`

`=>-(\sqrt{a}+6)/(3)<0`

Hay `P-1<0` 

Vậy `P<1`