Question

inequalities question ​

Answer 1

$\frac{ {x}^{2} + 2x - 3 }{ {x}^{2} + 1} < 0 \\ \\ \\ \frac{ {x}^{2} + 3x - x - 3 }{ {x}^{2} + 1} < 0 \\ \\ \\ \frac{(x + 3)(x - 1)}{ {x}^{2} + 1} < 0 \\ \\ \\ \frac{(x + 3)(x - 1)}{ {x}^{2} + 1} \times {x}^{2} + 1 < 0 \times {x}^{2} + 1 \\ \\ \\ (x + 3)(x - 1) < 0 \\ \\ \\ \frac{(x + 3)(x - 1) }{ {x}^{2} + 2x - 3} < \frac{0}{{x}^{2} + 2x - 3} \\ \\ 0 < 0$