[tex]\frac{4}{x - 6} + \frac{3}{x + 5} = \frac{4(x + 5)}{(x - 6)(x + 5)} + \frac{3(x - 6)}{(x - 6)(x + 5)} = \frac{4x + 20}{(x - 6)(x + 5)} = \frac{3x - 18}{(x - 6)(x + 5)} = \frac{4x + 20 + 3x - 18}{(x - 6)(x + 5)} = \frac{4x + 3x + 20 - 18}{(x - 6)(x + 5)} = \frac{7x + 2}{(x - 6)(x + 5)}[/tex]
