$\frac{x^2 - 16x}{(x - 7)^4} + \frac{2x + 49}{(7 - x)^4} = \frac{x^2 - 16x}{(x - 7)^4} + \frac{2x + 49}{(x - 7)^4} = \frac{x^2 - 16x + 2x + 49}{(x - 7)^4} = \frac{x^2 - 14x + 49}{(x - 7)^4} = \frac{(x - 7)^2}{(x - 7)^4} = \frac{1}{(x - 7)^2}$

$\frac{y^2 + y}{(y - 6)(y + 2)} + \frac{y + 36}{(6 - y)(2 + y)} = \frac{y^2 + y}{(y - 6)(y + 2)} - \frac{y + 36}{(y - 6)(y + 2)} = \frac{y^2 + y - y - 36}{(y - 6)(y + 2)} = \frac{y^2 - 36}{(y - 6)(y + 2)} = \frac{(y - 6)(y + 6)}{(y - 6)(y + 2)} = \frac{y + 6}{y + 2}$