Question

Cho biểu thức: P= \(\dfrac{\sqrt{a}+3}{\sqrt{a}-2}-\dfrac{\sqrt{a}-1}{\sqrt{a}+2}+\dfrac{4\sqrt{a}-4}{4-a}\)

a) Rút gọn P

b) Tính giá trị của P với a = 9

Answer 1

`P=(sqrta+3)/(sqrta-2)-(sqrta-1)/(sqrta+2)+(4sqrta-4)/(4-a)`

`đk:x>=0,x ne 4`

`P=(a+5sqrta+6-a+3sqrta-2-4sqrta+4)/(a-4)`

`=(4sqrta+8)/(a-4)`

`=4/(sqrta-2)`

`b)a=9`

`=>P=4/(3-2)=4`

Answer 2

a) Ta có: \(P=\dfrac{\sqrt{a}+3}{\sqrt{a}-2}-\dfrac{\sqrt{a}-1}{\sqrt{a}+2}+\dfrac{4\sqrt{a}-4}{4-a}\)

\(=\dfrac{\left(\sqrt{a}+3\right)\left(\sqrt{a}+2\right)-\left(\sqrt{a}-1\right)\left(\sqrt{a}-2\right)-4\sqrt{a}+4}{\left(\sqrt{a}-2\right)\left(\sqrt{a}+2\right)}\)

\(=\dfrac{a+5\sqrt{a}+6-a+3\sqrt{a}-2-4\sqrt{a}+4}{\left(\sqrt{a}-2\right)\left(\sqrt{a}+2\right)}\)

\(=\dfrac{4\sqrt{a}+8}{\left(\sqrt{a}-2\right)\left(\sqrt{a}+2\right)}\)

\(=\dfrac{4\left(\sqrt{a}+2\right)}{\left(\sqrt{a}+2\right)\left(\sqrt{a}-2\right)}=\dfrac{4}{\sqrt{a}-2}\)

b) Thay a=9 vào P, ta được:

\(P=\dfrac{4}{\sqrt{9}-2}=\dfrac{4}{3-2}=\dfrac{4}{1}=4\)

Vậy: khi a=9 thì P=4