Question

Упростите выражение
(y^-2-x^-2)^1*(x^-1-y^-1)

Answer 1

Решение
(y⁻¹)² - (x⁻¹)² + (y⁻¹ - x⁻¹) = (y⁻¹ - x⁻¹)*(y⁻¹ + x⁻¹) + (y⁻¹ - x⁻¹) =
= (y⁻¹ - x⁻¹)*(y⁻¹ + x⁻¹ + 1) = [(x - y)/xy]*[(x + y + xy)/xy] =
= [(x - y)*(x + xy + y)]/x²y²