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August 2022
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Artem112
Verified answer
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AlbuRin
( ( (a^2 + b^2)/b -a) : (1/a + 1/b)^(-1) ) * a^2b^2/(a^3 + b^3) =
1) (a^2 + b^2)/b - a = (a^2 - ab + b^2)/ab
2) (1/a + 1/b)^(-1) = ( (a + b)ab)^(-1) = ab/(a + b)
3) (a^2 - ab + b^2) * ab * a^2b^2 / (ab (a + b)(a + b)(a^2 - ab + b^2) ) = = a^2b^2 / (a +b)^2 = (ab/(a + b) )^2
Ответ. (ab/(a + b) )^2
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Answers & Comments
Verified answer
1) (a^2 + b^2)/b - a = (a^2 - ab + b^2)/ab
2) (1/a + 1/b)^(-1) = ( (a + b)ab)^(-1) = ab/(a + b)
3) (a^2 - ab + b^2) * ab * a^2b^2 / (ab (a + b)(a + b)(a^2 - ab + b^2) ) = = a^2b^2 / (a +b)^2 = (ab/(a + b) )^2
Ответ. (ab/(a + b) )^2