To solve the equation x : 3/2 + x : 6/7 - x : 2 = 1/12, we need to find the value of x.

First, let's simplify the equation by finding a common denominator for the fractions:

x : (3/2) + x : (6/7) - x : 2 = 1/12

The common denominator for 2, 7, and 12 is 84. So, we can rewrite the equation as:

84x : 42 + 84x : 12 - 42x : 84 = 7

Now, let's simplify each term:

(84x/42) + (84x/12) - (42x/84) = 7

Simplifying the fractions:

2x + 7x - x/2 = 7

Combining like terms:

9x - x/2 = 7

To get rid of the fraction, we can multiply both sides of the equation by 2:

2(9x - x/2) = 2(7)

18x - x = 14

17x = 14

Dividing both sides by 17:

x = 14/17

So, the solution to the equation is x = 14/17.

Regarding the second part of your question, it seems to be incomplete or unrelated to the equation provided. Could you please provide more information or clarify what you mean by "A = 1/2 + 1/4 =+ 1/6 + 1/32 + 1/64" and "3/3x7 + 3/7x11 + 3/11x15 + 3/15x19 + 3/19 x23"?