Question

Rút gọn biểu thức

D = \(\dfrac{1}{x-1}-\dfrac{1}{x+1}+\dfrac{4x+2}{x^2-1}\)

Tìm giá trị cỉa D = 9 + 4\(\sqrt{5}\)

Answer 1

\(D=\dfrac{x+1-x+1+4x+2}{\left(x-1\right)\left(x+1\right)}=\dfrac{4}{x-1}\)

Khi x=9+4căn 5 thì \(D=\dfrac{4}{8+4\sqrt{5}}=\dfrac{1}{\sqrt{5}+2}=\sqrt{5}-2\)