Question

Demonstrati ca -2 < 4x/x^2+1 < 2

Answer 1

$\it -2<\dfrac{4x}{x^2+1}<2|_{\cdot x^2+1} \Longrightarrow -2x^2-2<4x<2x^2+2|_{-4x} \Longrightarrow \\ \\ -2x^2-2-4x<0<2x^2+2+4x \Longrightarrow-2(x^2+2x+1)<0<2(x^2+2x+1)\Longrightarrow\\ \\ \Longrightarrow-2(x+1)^2<0<2(x+1)^2 \ \ \ \ (A)$