Oblicz wartość wyrażenia [latex] frac{ sqrt{a}+ sqrt{b} }{a-b} : frac{a*b}{ sqrt{a}- sqrt{b} } [/latex] dla a = 3+√2 i b= 3 -√2

[latex] frac{ sqrt{a}+ sqrt{b} }{a-b} : frac{a*b}{ sqrt{a}- sqrt{b} }= \ =frac{ sqrt{a}+ sqrt{b} }{a-b} * frac{sqrt{a}- sqrt{b}}{ a*b} } = frac{ sqrt{a}^{2}- sqrt{b} ^{2} }{a^2b-ab^2} = \= frac{a-b}{a^2b-ab^2} = frac{a-b}{(ab)(a-b)}= frac{1}{ab} = frac{1}{(3+ sqrt{2})(3- sqrt{2}) }=\ \= frac{1}{9-2} = frac{1}{7} [/latex]