Question

A= (1+\(\frac{x^2}{X^2+1}\)) : (\(\frac{1}{x-1}\)- \(\frac{2x}{x^3+x-x^2-1}\))

a, Rút gọn A

b, A=? khi x= \(\frac{-1}{2}\)

c, x=? để A< 1

d, Tìm x\(\varepsilon\)Z để A\(\varepsilon\)Z

Answer 1

Bạn cần câu nào?

Answer 2

làm đc câu nào hay câu đây, càng nhiều càng tốt

cảm ơn nha

Answer 3

a. \(A=\left(\frac{2x^2+1}{x^2+1}\right):\left(\frac{1}{x-1}-\frac{2x}{\left(x^2+1\right)\left(x-1\right)}\right)\)

\(\Rightarrow A=\frac{2x^2+1}{x^2+1}:\left(\frac{x^2+1-2x}{\left(x-1\right)\left(x^2+1\right)}\right)\)

\(\Rightarrow A=\frac{2x^2+1}{x^2+1}:\left(\frac{\left(x-1\right)^2}{\left(x-1\right)\left(x^2+1\right)}\right)\)

\(\Rightarrow A=\frac{2x^2+1}{x^2+1}:\frac{x-1}{x^2+1}\)

\(\Rightarrow A=\frac{2x^2+1}{x^2+1}\cdot\frac{x^2+1}{x-1}\)\(\Rightarrow A=\frac{2x^2+1}{x-1}=\left(2x+2\right)+\frac{3}{x-1}\)