[tex]\cfrac{2}{x^2-25}~~ - ~~\cfrac{3x}{x^2-4x-5}\implies \cfrac{2}{\underset{\textit{difference of squares}}{x^2-5^2}}~~ - ~~\cfrac{3x}{(x+1)(x-5)} \\\\\\ \cfrac{2}{(x-5)(x+5)}~~ - ~~\cfrac{3x}{(x+1)(x-5)}\implies \cfrac{(x+1)2~~ - ~~(x+5)3x}{\underset{\textit{using this LCD}}{(x+1)(x-5)(x+5)}} \\\\\\ \cfrac{2x+2-3x^2-15x}{(x+1)(x-5)(x+5)}\implies \cfrac{2-3x^2-13x}{(x+1)(x-5)(x+5)}\qquad x\ne -1,\pm 5[/tex]
why can't it be -1 or 5 or -5? if it ever does become that, the denominator will go poof and the fraction undefined.
