Question 1055130
<pre>
1/[1+1/(1-1/x)]=2

 {{{matrix(3,3, 1/(1 + 1/(1 - 1/x)), "=", 2,
1/(1 + 1/((x - 1)/x)), "=", 2,
1/(1 + x/(x - 1)), "=", 2)}}}

1 ÷ {{{matrix(1,3, (1 + x/(x - 1)), "=", 2)}}}
1 ÷ {{{matrix(1,3, ((x - 1 + x)/(x - 1)), "=", 2)}}}
  1 ÷ {{{matrix(1,3, ((2x - 1)/(x - 1)), "=", 2)}}}
 {{{matrix(1,5, 1, "*", ((x - 1)/(2x - 1)), "=", 2)}}}
        {{{matrix(1,3, (x - 1)/(2x - 1), "=", 2)}}}
          x - 1 = 2(2x - 1) --- Cross-multiplying, or multiplying by LCD, 2x - 1
          x - 1 = 4x - 2
         x - 4x = - 2 + 1
           - 3x = - 1
             {{{highlight_green(matrix(1,5, x, "=", (- 1)/(- 3), "=", highlight(1/3)))}}}

As usual, the person named JOGS/JOSG is AGAIN INCORRECT, as he normally is. Therefore, ONCE AGAIN,
IGNORE his solution, if it can be called that!</pre>