Resposta :
=
1 = 1 = a^2b^2 ==> a^2b^2(a+b)^-2
[ 1 + 1 ]^2 (b + a )^2 (a+b)^2
a b a^2b^2
1 = 1 = a^2b^2 ==> a^2b^2(a+b)^-2
[ 1 + 1 ]^2 (b + a )^2 (a+b)^2
a b a^2b^2
Olá, Tete.
[tex](a^{-1}+b^{-1})^{-2}=\\\\=\frac1{(\frac1a+\frac1b)^2}=\\\\=\frac1{(\frac{b+a}{ab})^2}=\\\\=\frac{1}{\frac{(a+b)^2}{a^2b^2}}=\\\\=\frac{a^2b^2}{(a+b)^2}=\\\\=\boxed{(\frac{ab}{a+b})^2}[/tex]
[tex](a^{-1}+b^{-1})^{-2}=\\\\=\frac1{(\frac1a+\frac1b)^2}=\\\\=\frac1{(\frac{b+a}{ab})^2}=\\\\=\frac{1}{\frac{(a+b)^2}{a^2b^2}}=\\\\=\frac{a^2b^2}{(a+b)^2}=\\\\=\boxed{(\frac{ab}{a+b})^2}[/tex]