Question

cho M = \(\dfrac{x+12}{x-4}\)+ \(\dfrac{1}{\sqrt{ }x+2}\)- \(\dfrac{4}{\sqrt{ }x-2}\)

1, rút gọn

2, tính M khi x=4 + 2\(\sqrt{x}\)

Answer 1

\(M=\dfrac{x+12}{x-4}+\dfrac{1}{\sqrt{x}+2}-\dfrac{4}{\sqrt{x}-2}\)

\(M=\dfrac{x+12}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}+\dfrac{1}{\sqrt{x}+2}-\dfrac{4}{\sqrt{x}-2}\)

\(M=x+12+\sqrt{x}-2-4\left(\sqrt{x}+2\right)\)

\(M=x+12+\sqrt{x}-2-4\sqrt{x}-8\)

\(M=x-3\sqrt{x}+2\)

\(M=x-\sqrt{x}-2\sqrt{x}+2\)

\(M=\sqrt{x}\left(\sqrt{x}-1\right)-2\left(\sqrt{x}-1\right)\)

\(M=\left(\sqrt{x}-1\right)\left(\sqrt{x}-2\right)\)