Question

Solution for the inequation:
2x / 2x^2 + 5x + 2 > 1 / x + 1 ?

Answer 1

2x/(2x² + 5x + 2) > 1/(x +1)

=2x/(2x² + 5x +2) - 1/(x +1) > 0

={2x(x +1)- (2x² + 5x +2) }/(2x² + 5x +2)(x +1) >0
[ use, (2x² +5x +2) = (x +2)(2x +1) ]

={2x² + 2x -2x² -5x -2 }/(2x +1)(x +2)(x +1)>0

= (3x + 2)/(2x +1)(x +2)(x +1) < 0

solve this by using wave curve,

then ,
x € (-∞ , -2) U ( -1, -2/3) U ( -1/2 , ∞)