Вправи 401 - 467 » 403 (1-6)

403. Спростіть вираз: 1) a^2/(a+b) – b2(a + b)–1 = a^2/(a+b) – b^2/(a+b) = (a^2- b^2)/(a+b) = ((a-b)(a+b))/(a+b) = a – b; 2) 1/(x+y) – x(x + y)–2 = 1^(\x+y)/(x+y) – x/〖(x+y)〗^2 = (x+y-x)/〖(x+y)〗^2 = y/〖(x+y)〗^2 ; 3) 〖2m〗^3/(m+1) – 2m3(1 – m2)–1 = 〖2m〗^3/(m+1) – 〖2m〗^3/〖1-m〗^2 = 〖2m〗^(3^(\1+m) )/(1+m) – 〖2m〗^3/((1-m)(1+m)) = (〖2m〗^3+ 〖2m〗^3+ 〖2m〗^4- 〖2m〗^3)/((1-m)(1+m)) = 〖2m〗^4/〖1-m〗^2 ; 4) 4(a – 2)–1 – a^2/(a-2) = 4/(a-2) – a^2/(a-2) = 〖4-a〗^2/(a-2) = ((2-a)(2+a))/(a-2) = –((a-2)(a+2))/(a-2) = a – 2 5) (x – 5)–1 + x(x – 5)–1 – 6/(x+5) = 1/(x-5) + x/(x-5) – 6) (x + y)–2 – (x – y)–2 = 1^(\〖(x-y)〗^2 )/〖(x+y)〗^2 – 1^(\〖(x+y)〗^2 )/〖(x-y)〗^2 = (x^2- 2xy+ y^2- (x^2+ 2xy+ y^2))/( 〖(x+y)〗^2 (〖x-y)〗^2 ) = (x^2- 2xy+ y^2- x^2- 2xy- y^2)/(〖(x+y)〗^2 • 〖(x-y)〗^2 ) = –4xy/(〖(x+y)〗^2 〖(x-y)〗^2 ) ;