solve for x x-5/7 + x+8/5 = 9/7?

Multiply everything by 35:

35x-25+35x+56=45
70x+31=45
70x=14
x=14/70
x=1/5

(x - 5)/7 + (x + 8)/5 = 9/7
35[(x - 5)/7 + (x + 8)/5] = 35[9/7]
5(x - 5) + 7(x + 8) = 5[9]
5x - 25 + 7x + 56 = 45
5x + 7x = 45 + 25 - 56
12x = 14
x = 14/12
x = 7/6

Do you mean :-
(x - 5) / 7 + (x + 8) / 5 = 9 / 7 ???????
5x - 25 + 7x + 56 = 45
12x = 14
x = 14 / 12
x = 7 / 6

As you have typed the question , it reads :-
x - (5/7) + x + (8/5) = 9/7
35x - 25 + 35x + 56 = 45
70x = 14
70x = 14
x = 1 / 5

x-5/7 + x+8/5 = 9/7

2x = 9/7 + 5/7 - 8/5

2x = (45/35) + (25/35) - (56/35)

2x = 14/35

(2x) / 2 = (14/35) / 2

x = 14 / (35*2)

x = 14 / 70

x = 1 / 5