( 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 ).
