Question

$\frac{x+1}{x-2} + \frac{x}{x+3} - \frac{2 x^{2} +x}{ x^{2} +x-6}$

Answer 1

$\displaystyle \frac{x+1}{x-2} + \frac{x}{x+3} - \frac{2x^2+x}{x^2+x-6} = \frac{x+1}{x-2} + \frac{x}{x+3} - \frac{2x^2+x}{(x+3)(x-2)} = \\ \\ = \frac{(x+1)(x+3)+x(x-2)-2x^2-x}{(x+3)(x-2)} = \\ \\ =\frac{x^2+3x+x+3+x^2-2x-2x^2-x}{(x+3)(x-2)} = \frac{x+3}{(x+3)(x-2)} = \frac{1}{x-2}$