Question

Giúp em với !!!!!!!!!

Answer 1

a) \(P=\dfrac{2\sqrt{x}}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}-\dfrac{2}{\sqrt{x}+3}\)

= \(\dfrac{2\sqrt{x}-2\left(\sqrt{x}-3\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}=\dfrac{6}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}\)

b) Xét \(A=\dfrac{P}{Q}=\dfrac{\dfrac{6}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}}{\dfrac{6}{\sqrt{x}\left(\sqrt{x}-3\right)}}=\dfrac{\sqrt{x}}{\sqrt{x}+3}\)

Xét \(A^2-A=A\left(A-1\right)\)

Có A \(>0\) ; \(A-1=\dfrac{\sqrt{x}}{\sqrt{x}+3}-1=\dfrac{-3}{\sqrt{x}+3}< 0\)

=> A(A-1) \(< 0\)

=> A²  \(< A\)