Verified answer

(5/ x + 1) − (1/ 2) = (1 /6x + 6)

(5/ x + 1) − (1/ 2) = (1 /6(x + 1))

(5/ x + 1) - (1 /6(x + 1)) = 1/2

(30-1) / 6(x+1) = 1/2

(29/6) * 2 = x+1

29/3 - 1 = x

26/3 = x

x = 26/3

I was a little confused by the punctuation so I'll rewrite this. Let me know if i misinterpreted.

5/(x+1) - 1/2 = 1/(6x+6)

Rewrite the right side to be 1/(6*(x+1)) which gives you a common denominator. Now get everything on one side...

5/(x+1) - 1/2 - 1/(6*(x+1)) = 0

multiply both sides by 6 to simplify the bottom

30/(x+1) - 6/2 - 1/(x+1) = 0

simplify to get

29/(x+1) - 3 = 0

now just solve for x

29/(x+1) = 3

29 = 3(x+1)

29/3 = x+1

29/3 - 1 = x

29/3 - 3/3 = x

26/3 = x

Final answer is x = 26/3

The question is not clear so, I will answer in different aspect:

1. if 1/6x is separate and +6 is separate in Right hand side and 5/x is separate and +1 is seperate in Left hand side

(5/x)+1-(1/2) = (1/6x) +6

or, (5/x)-(1/6x) = 6-1+(1/2)

or, (6*5 - 1)/6x = 5 + (1/2)

or, 29/6x = (10 +1)/2

or (29 * 2)/11 = 6x;

or, 58/(11*6) = x

or, x = 58/66

2. if 1 is separate and 6x+6 is separate then the procedure is like the answer before mine.

or, x = 29/11

5/(x+ 1) - 1/2 = 1/(6x + 6)

29 = 3(x + 1)

26 = 3x => x = 26/3

(5/ x + 1) − (1/ 2) = (1 /6x + 6)

(5/ x + 1) − (1/ 2) = (1 /6(x + 1))

(5/ x + 1) - (1 /6(x + 1)) = 1/2

(30-1) / 6(x+1) = 1/2

29/ 6(x+1) = 1/2

29*2 = 6(x+1) [ cross multiplying]

58 = 6(x+1)

58/6 = x+1

9.67 = x+1

x = 9.67 -1

x = 8.67