• докажите тождество 1/(y-1)(y-2) + 1/(y-2)(y-3) + 1/(y-3)(y-4) = 3/(y-1)(y-4)

Ответы 1

  • 1/((y-1)(y-2)) + 1/((y-2)(y-3)) + 1/((y-3)(y-4)) = 3/((y-1)(y-4)),

    1/((y-1)(y-2)) + 1/((y-2)(y-3)) + 1/((y-3)(y-4)) =

    = ((y-3)(y-4)+(y-1)(y-4)+(y-1)(y-2))/((y-1)(y-2)(y-3)(y-4)) =

    = ((y-4)(y-3+y-1)+(y-1)(y-2))/((y-1)(y-2)(y-3)(y-4)) =

    = ((y-4)(2y-4)+(y-1)(y-2))/((y-1)(y-2)(y-3)(y-4)) =

    = (2(y-4)(y-2)+(y-1)(y-2))/((y-1)(y-2)(y-3)(y-4)) =

    = (y-2)(2(y-4)+y-1)/((y-1)(y-2)(y-3)(y-4)) =

    = (2y-8+y-1)/((y-1)(y-3)(y-4)) =

    = (3y-9)/((y-1)(y-3)(y-4)) =

    = 3(y-3)/((y-1)(y-3)(y-4)) =

    = 3 /((y-1)(y-4))

    • Автор:

      acejhgd
    • 5 лет назад
    • 0
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