Question

P = (\(\dfrac{2\sqrt{x}}{\sqrt{x}}-\dfrac{x-4}{\sqrt{x}+2}\)). \(\dfrac{1}{\sqrt{x}-2}\)

a Tìm đkxđ rồi rút gọn P

b Tìm x để P = \(\dfrac{2}{3}\)

c Tính p khi x = 8\(-\)2\(\sqrt{7}\)

Answer 1

a: ĐKXĐ: x>0; x<>4

\(P=\left(2-\sqrt{x}+2\right)\cdot\dfrac{1}{\sqrt{x}-2}=\dfrac{4-\sqrt{x}}{\sqrt{x}-2}\)

b: P=2/3

=>(4-căn x)/(căn x-2)=2/3

=>2căn x-4=12-3căn x

=>5căn x=16

=>x=256/25

c: Khi x=8-2căn 7 thì \(P=\dfrac{4-\sqrt{7}+1}{\sqrt{7}-1-2}=\dfrac{5-\sqrt{7}}{\sqrt{7}-3}=-4-\sqrt{7}\)