Question

For what real x, can we have the inequality I4x-x²-3I / √(x+1) >0

Answer 1

$\mid$ 4x-x²-3$\mid$ /(x+1)^1/2 >0 $\to$ $\mid$-x²+4x-3$\mid$ /(x+1)^1/2 >0 $\to$ $\mid$ -x²+3x+x-3$\mid$ /(x+1)^1/2 >0 $\to$ $\mid$ (-x+1)(x-3)$\mid$/(x+1)^1/2 >0 identifying the intervals -1<x<1 or 1<x<3 or x>3 ,finding non-negative value for radical x is greater or equal to -1 ,Merging overlapping intervals, the solution is (-1,1)U(1,3)U(3, $\infin$ )