solve -x/x +1 = -3/x +7

the first answer is the correct answer to the question you asked.

The second is the correct answer to the question that you may have intended to ask.   :)

-X/x+1=-3/x+7

-1+1=-3/x+7

0=-3/x+7

(3/x=7)multiply byX

3=7x

x=3/7

If this is the problem:  -1 / (x + 1)  =  -3 / (x + 7)

Cross-multiply:            -1 · (x + 7)  =  -3 · (x + 1)

Simplify:                             -x - 7  =  -3x - 3

Add  3x  to both sides:         2x - 7  =  -3

Add  7  to both sides:                2x  =  4

Divide by 2:                                x  =  2