Вправи 201 - 342 » 246

246. Подайте у вигляді дробу вираз: 1) ab–1 + a–1b = a^(\a)/b + b^(\b)/a = (a^2+ b^2)/ab; 2) 3a–1 + ab–2 = 3^(\b)/a + a^(\a)/b^2 = (3b^2+ a^2)/(ab^2 ); 3) m2n2(m–3 – n–3) = m2n2(1/m^3 – 1/n^3 ) = (m^2 n^2)/1 • (n^3- m^3)/(m^3 n^3 ) = (n^3- m^3)/mn; 4) (a + b)–1 • (a–1 + b–1) = 1/(a+b) • (1^(\b)/a + 1^(\a)/b) = 1/(a+b) • (b+a)/ab = 1/ab; 5) (c–2 – d–2) : (c + d) = (1^(\d^2 )/c^2 – 1^(\a^2 )/d^2 ) : (c + d) = (d^2- c^2)/(c^2 d^2 ) • 1/(c+d) = ((d-c)(d+c) • 1)/(c^2 d^2 (c+d)) = (d-c)/(c^2 d^2 ); 6) (xy–2 + x–2y) • ((x^2- xy+ y^2)/x)–1 = (x/y^2 + y/x^2 ) • x/(x^2- xy+ y^2 ) = (x^3+ y^3)/(y^2 x^2 ) • x/(x^2- xy+ y^2 ) = ((x+y)(x^2- xy+ y^2 ) • x)/(x^2 y^2 (x^2- xy+ y^2)) = (x+y)/(xy^2 ).