Question

Выполните вычитание дробей :
a-b/a+b-b+a/a-b

/-это дробь

Answer 1

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

Answer 2

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