Вправи 401 - 467 » 417 (1)

417. Спростіть вираз: 1) 〖(1+x)〗^(-1)/(x+2) + 〖(2+x)〗^(-1)/(x+3) + 〖(3+x)〗^(-1)/(x+4) = 1/((x+1)(x+2)) + 1/((x+2)(x+3)) + 1/((x+3)(x+4)) = ((x+3)(x+4)+ (x+1)(x+4)+ (x+1)(x+2))/((x+1)(x+2)(x+3)(x+4)) = (x^2+ 4x+3x+12+ x^2+ 4x+x+4+x^2+ 2x+x+2)/((x+1)(x+2)(x+3)(x+4)) = (〖3x〗^2+ 15x+18)/((x+1)(x+2)(x+3)(x+4)) = (〖3(x〗^2+ 5x+6) )/((x+1)(x+2)(x+3)(x+4)) = (〖3(x〗^2+ 2x+3x+6))/((x+1)(x+2)(x+3)(x+4)) = (3(x(x+2)+ 3(x+2)))/((x+1)(x+2)(x+3)(x+4)) = (3(x+2)(x+3))/((x+1)(x+2)(x+3)(x+4)) = 3/((x+1)(x+4)).