Question

Solve the following inequalities
$\frac{x+1}{x+5}+\frac{x}{x-1}<\frac{2x^2+5x}{x^2+4x-5}$

Answer 1

$\frac{x+1}{x+5}+\frac{x}{x-1}<\frac{2x^2+5x}{x^2+4x-5}$

$\Rightarrow \frac{x^2-1^2+x(x+5)}{(x+5)(x-1)}<\frac{2x^2+5x}{x^2+4x-5}$

$\Rightarrow \frac{x^2-1+x^2+5x}{x^2+4x-5}<\frac{2x^2-5x}{x^2+4x-5}$

$\Rightarrow 2x^2+5x-1<2x^2+5x$

$\Rightarrow -1<0$ which is true $\forall xϵR$.