( x² - 1 ) / ( x² + 5 x + 4 ) < 0 x² + 5 x + 4 = x² + 4 x + x + 4 = x ( x + 4 ) + ( x + 4 ) = ( x + 4 ) ( x + 1 ) Therefore: ( x - 1 ) ( x + 1 ) / ( x + 4 ) ( x + 1 ) < 0 ( x -1 ) / ( x + 4 ) < 0 1. x - 1 > 0 and x + 4 < 0 x > 1 and x < - 4 ( not possible ) 2. x - 1 < 0 and x + 4 > 0 x < 1 and x > - 4 Answer: x ∈ ( - 4, 1 ).