Question 189475
{{{ (x+1)/(2x) = (x-1)/(2x-1) }}} Start with the given equation



{{{ (x+1)(2x-1) = 2x(x-1) }}} Cross multiply



{{{ (x+1)(2x-1) = 2x^2-2x }}} Distribute



{{{ 2x^2-x+2x-1 = 2x^2-2x }}} FOIL



{{{ 2x^2-x+2x-1 - 2x^2 + 2x =0 }}} Get everything to the left side



{{{ 3x-1 =0 }}} Combine like terms.



{{{ 3x=1 }}} Add 1 to both sides



{{{ x=1/3 }}} Divide both sides by 3 to isolate "x"



So the solution is {{{x=1/3}}} which in decimal form is *[Tex \LARGE x = 0.\overline{3}] which approximates to *[Tex \LARGE x \approx 0.333\ldots]