Question

[Kamado Tanjirou ๖ۣۜ( ๖ۣۜTεαм ƙɦĭêηɠ...]

Cho biểu thức:

\(A=\left(\dfrac{\sqrt{x}+3}{\sqrt{x}-2}+\dfrac{\sqrt{x}+2}{3-\sqrt{x}}+\dfrac{\sqrt{x}+2}{x-5\sqrt{x}+6}\right):\left(\dfrac{x-2}{x-\sqrt{x}-2}-1\right)\)

a) Rút gọn A.

b) Tìm x để P=2A - \(\dfrac{1}{x}\)đạt GTLN.

Answer 1

[Nguyễn Hoàng Minh]

\(a,A=\dfrac{x-9-x+4+\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}:\dfrac{x-2-x+\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+1\right)}\\ A=\dfrac{\sqrt{x}-3}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}\cdot\dfrac{\left(\sqrt{x}-2\right)\left(\sqrt{x}+1\right)}{\sqrt{x}}\\ A=\dfrac{\sqrt{x}+1}{\sqrt{x}}\)

Answer 2

[Kamado Tanjirou ๖ۣۜ( ๖ۣۜTεαм ƙɦĭêηɠ...]

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