Question

$\frac{2x}{2x^2+5x+2}>\frac{1}{(x+1)}$

Answer 1

R.E.F image

$\frac{2x}{2x^2+5x+2}>\frac{1}{x+1}$

$\frac{2x}{2x^2+5x+2}-\frac{1}{x+1}>0$

$\frac{2x(x+1)-(2x^2+5x+2)}{(2x^2+5x+2)(x+1)}>0$

$\frac{2x^2+2x-2x^2-5x-2}{(2x^2+4x+x+2)(x+1)}>0$

$\frac{-3x-2}{\left[2x\right(x+2)+(x+2\left)\right](x+1)}>0$

$\frac{-3x-2}{(x+2)(2x+1)(x+1)}>0$

$\frac{3x+2}{(x+2)(2x+1)(x+1)}>0$

$\therefore xϵ(-\infty ,-2)\cup (-1,-2/3)\cup (-1/2,\infty )$