perform the indicated operations and simplify x-5/x-7-x-1/x+7+x-35/x^2-49

Answer 1

If what you typed means

(x-5)/(x-7) - (x-1)/(x+7) + (x-35)/(x^2-49) then

put everything over a common denominator. In this case, since x^2 - 49 = (x-7)(x+7) that will be our LCD.

The numerator will then be:
(x-5)(x+7) - (x-1)(x-7) + (x-35)
= x^2 + 2x - 35 - (x^2 - 8x + 7) + (x - 35)
= (11x - 77)
= 11(x-7)

Put that over (x-7)(x+7) and you have

11(x-7) / (x-7)(x+7)
= 11/(x+7)

Answer 2

You need to clarify your formula by spacing and/or parentheses.

x - 5/x - 7 - x - 1/x + 7 + x - 35/x^2 - 49 (?)

x - 5/(x-7) - x - 1/(x-7) + x 35/(x^2-49) (?)