Question

Explain why the inequalities x + 1 / x - 1 < x +3 / x + 2 and x + 5 / (x - 1)(x + 2) < 0 are equivalent

Answer 1

\[\frac{x+1}{x-1} < \frac{x+3}{x+2}\]
\[\frac{x+1}{x-1} - \frac{x+3}{x+2} < 0\]
\[\frac{(x+1)(x+2)-(x+3)(x-1)}{(x-1)(x+2)}<0\]
\[\frac{x^2+3x+2-x^2-2x+3}{(x-1)(x+2)}<0\]
\[\frac{x+5}{(x-1)(x+2)}<0\]

Answer 2

how do u explain it?