Potęgi Wykonaj działanie [latex] frac{( 7^{ frac{1}{2} } - 9^{ frac{1}{2} } ) ( sqrt{7} +3)}{( 12^{ frac{1}{2} } - 3^{ frac{1}{2} } ) ^{2} } [/latex]

[latex]dfrac{(7^{frac{1}{2}}-9^{frac{1}{2}})(sqrt{7}+3)}{(12^{frac{1}{2}}-3^{frac{1}{2}})^2}=dfrac{(sqrt{7}-3)(sqrt{7}+3)}{(sqrt{12}-sqrt{3})^2}=\ =dfrac{(sqrt{7})^2-3^2}{(sqrt{12})^2-2 cdot sqrt{12} cdot sqrt{3}+(sqrt{3})^2}=dfrac{7-9}{12-2sqrt{36}+3}=dfrac{-2}{15-2 cdot 6}=\ [/latex] [latex]=dfrac{-2}{15-12}=-dfrac{2}{3} \ oxed{(a+b)(a-b)=a^2-b^2} \ oxed{(a-b)^2=a^2-2ab+b^2}[/latex]