Вправи 101 - 200 » 166 (1-5)

166. Спростіть вираз: 1) (x\y + x/y) : (x\y – x/y) = (xy+x)/y : (xy-x)/y = (x(y+1) • y)/(y •x (y-1)) = (y+1)/(y-1); 2) (a^(\a-b)/b + (a+ b^(\b))/(a-b)) •(ab^2)/(a^2+ b^2 ) = (a(a-b)+ b(a+b))/(b(a-b)) • (ab^2)/(a^2+ b^2 ) = (a^2- ab+ab+ b^2)/(b(a-b)) • (ab^2)/(a^2+ b^2 ) = ((a^2+ b^2 )ab^2)/(b(a-b)(a^2+ b^2)) = ab/(a-b); 3) (m/(mm-1) – 1\m–1) : m/(mn-n) = ((m-(m-1)) • n(m-1))/((m-1) • m) = ((m-m+1) • n(m-1))/((m-1) • m) = n/m; 4) (a/b – b/a) • 4ab/(a-b) = (a^2- b^2)/ab • 4ab/(a-b) = ((a-b)(a+b) • 4ab)/(ab(a-b)) = 4a + 4b; 5) a/b – (a^2- b^2)/b^2 : (a+b)/b = a/b – ((a-b)(a+b) • b)/(b^2 (a+b)) = a/b – (a-b)/b = (a-a+b)/b = b/b = 1;