Question

Сократите дроби: a^3 - b^3/a^4 - b^4

Answer 1

$\frac{a ^{3} -b ^{3} }{a ^{4} -b ^{4} } = \frac{(a-b)(a ^{2} +b ^{2} +ab)}{(a ^{2} -b ^{2} )(a ^{2} +b ^{2} )} =\frac{(a-b)(a ^{2} +b ^{2} +ab)}{(a-b)(a+b)(a ^{2} +b ^{2} )} = \\ \\ =\frac{(a ^{2} +b ^{2} +ab)}{(a+b)(a ^{2} +b ^{2} )}$