Can someone explain how we solve this problem

X + 5 - 1/x = x - 7 + 1/x
Bring x + 5 - 1/x together using the common denominator x. Bring x - 7 + 1/x together using the common denominator x:
(x^2 + 5 x - 1)/x = (x^2 - 7 x + 1)/x
Multiply both sides by x:
x^2 + 5 x - 1 = x^2 - 7 x + 1
Subtract x^2 - 7 x + 1 from both sides:
12 x - 2 = 0
Factor constant terms from the left hand side:
2 (6 x - 1) = 0
Divide both sides by 2:
6 x - 1 = 0
Add 1 to both sides:
6 x = 1
Divide both sides by 6:
  x = 1/6