Question

cho BT

A= \(\dfrac{4}{\sqrt{x}-2}\)+ \(\dfrac{2}{\sqrt{x}+2}\)+ \(\dfrac{4\sqrt{x}+6}{4-x}\)

a, rút gọn A

b, tìm giá trị của A khi x=\(7-4\sqrt{3}\)

c, tìm Min P=A\(\times\)(x+5)

Answer 1

a) \(A=\dfrac{4}{\sqrt{x}-2}+\dfrac{2}{\sqrt{x}+2}+\dfrac{4\sqrt{x}+6}{4-x}\)

\(A=\dfrac{4}{\sqrt{x}-2}+\dfrac{2}{\sqrt{x}+2}-\dfrac{4\sqrt{x}+6}{x-4}\)

\(A=\dfrac{4}{\sqrt{x}-2}+\dfrac{2}{\sqrt{x}+2}-\dfrac{4\sqrt{x}+6}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)

\(A=\dfrac{4\left(\sqrt{x}+2\right)+2\left(\sqrt{x}-2\right)-\left(4\sqrt{x}+6\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)

\(A=\dfrac{4\sqrt{x}+8+2\sqrt{x}-4-4\sqrt{x}-6}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)

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