Answer
$\frac{-x^3-3x^2-x-51}{x^3+3x^2-25x-75}$
Work Step by Step
Write each rational expression using the least common denominators and then simplify:
$\frac{x+3}{x^2-25}-\frac{x-1}{x-5}+\frac{3}{x+3}$
$=\frac{(x+3)(x+3)}{(x^2-5)(x+3)}-\frac{(x+5)(x-1)(x+3)}{(x+5)(x-5)(x+3)}+\frac{(x^2-25)(3)}{(x^2-25)(x+3)}$
$=\frac{x^2+6x+9}{(x+5)(x-5)(x+3)}-\frac{x^3+7x^2+7x-15}{(x+5)(x-5)(x-3)}+\frac{3x^2-75}{(x+5)(x-5)(x+3)}$
$=\frac{-x^3-3x^2-x-51}{x^3+3x^2-25x-75}$
