Question 189475
{{{ (x+1)/2x = (x-1)/(2x-1) }}}
You must multiply each side of the equation by the same 
thing so that the equation is still true.
What you should multiply each side by is {{{2x*(2x - 1)}}}
{{{ 2x*(2x - 1)*((x+1)/2x) = 2x*(2x - 1)*((x-1)/(2x-1)) }}}
On the left side, the {{{2x}}}'s cancel, and on the right
side, the {{{2x - 1}}}'s cancel
{{{ (2x - 1)*(x+1) = 2x*(x-1) }}}
{{{2x^2 + x - 1 = 2x^2 - 2x}}}
Subtract {{{2x^2}}} from both sides
{{{x - 1 = -2x}}}
{{{3x = 1}}}
{{{x = 1/3}}} answer
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check answer:
{{{ (x+1)/2x = (x-1)/(2x-1) }}}
{{{ (1/3+1)/(2*(1/3)) = (1/3-1)/(2*(1/3)-1) }}}
{{{ (4/3)/(2/3) = (-2/3)/(-1/3) }}}
Multiply both sides by {{{3/3}}}
{{{ (3/3)*((4/3)/(2/3)) = (3/3)*((-2/3)/(-1/3)) }}}
{{{4/2 = -2/-1}}}
{{{2 = 2}}}
OK