Wykonaj działanie: [latex] frac{2}{n+2} + frac{n+3}{ n^{2} -4 } - frac{3n+1}{ n^{2} - 4n +4 } [/latex] Odp: -14n/(n+2)(n-2)2

[latex] frac{2}{n+2} + frac{n+3}{n^{2}-4}- frac{3n+1}{n^{2}-4n+4} = frac{2(n-2)}{(n+2)(n-2)} + frac{n+3}{n^{2}-4}- frac{3n+1}{n^{2}-4n+4}= \ \ =frac{2n-4}{n^{2}-4}+ frac{n+3}{n^{2}-4}- frac{3n+1}{n^{2}-4n+4}= frac{3n-1}{n^{2}-4}- frac{3n+1}{n^{2}-4n+4} = \ \ = frac{3n-1}{(n+2)(n-2)} - frac{3n+1}{(n-2)^{2}} = frac{(3n-1)(n-2)}{(n+2)(n-2)(n-2)} - frac{(3n+1)(n+2)}{(n+2)(n-2)(n-2)} =[/latex] [latex]frac{3n^{2}-7n+2}{(n+2)(n-2)^{2}} - frac{3n^{2}+7n+2}{(n+2)(n-2)^{2}} = frac{3n^{2}-7n+2-3n^{2}-7n-2}{(n+2)(n-2)^{2}} = frac{-14n}{(n+2)(n-2)^{2}} [/latex]