[latex](frac{x+5}{(x-9)(x+9)}+ frac{x+7}{(x-9)^2} )( frac{x-9}{x+3} )^2+ frac{7+x}{9+x}= \=(frac{(x+5)(x-9)}{(x-9)^2(x+9)}+ frac{(x+7)(x+9)}{(x-9)^2(x+9)} ) frac{(x-9)^2}{(x+3)^2} + frac{7+x}{9+x}= \ = frac{(x+5)(x-9)+ (x+7)(x+9)}{(x-9)^2(x+9)} frac{(x-9)^2}{(x+3)^2}+ frac{7+x}{9+x}= \ = frac{x^2 -9x+5x-45+x^2+9x+7x+63}{x+9} frac{1}{(x+3)^2}+ frac{7+x}{9+x}= \ = frac{2x^2 +12x+18}{(x+9)(x+3)^2} + frac{7+x}{9+x}=frac{2(x^2 +6x+9)}{(x+9)(x+3)^2} + frac{7+x}{9+x}=[/latex][latex]=frac{2(x +3)^2}{(x+9)(x+3)^2} + frac{7+x}{9+x}=frac{2}{(x+9)} + frac{7+x}{9+x}=frac{2 +7+x}{9+x}=frac{9+x}{9+x}=1[/latex]