Question

Solve the following inequality:
$\frac{14x}{x+1}-\frac{9x-30}{x-4}<0$

Answer 1

$\frac{14x}{x+1}-\frac{9x-30}{x-4}<0$

$\frac{14x(x-4)-(9x-30)(x-1)}{(x+1)(x-4)}<0$

$\frac{14x^2-56x-(9x^2+9x-30x-30)}{x^2-4x+x-4}<0$

$\frac{14x^2-56x-9x^2-9x+30x+30}{(x+1)(x-4)}<0$

$\frac{5x^2-35x+30}{(x+1)(x-4)}<0$

$\frac{x^2-7x+6}{(x+1)(x-4)}<0$

$\frac{x^2-6x-x+6}{(x+1)(x-4)}<0$

$\frac{(x-6)(x-1)}{(x+1)(x-4)}<0(x=7\frac{1\times 6}{8\times 3}>0)$

$x\epsilon (-1,1)(4,6)$