Question 35539
{{{(2y)/( y - 4) - 3/ 5 = 3}}}


Start by adding {{{3/5}}} to each side of the equation:
{{{(2y)/( y - 4)  = 3+3/5 }}}
{{{(2y)/( y - 4)  = 18/5 }}}


Now, since {{{a/b=c/d}}} means the same as {{{a*d=b*c}}}, it follows that 
{{{(2y)/( y - 4)  = 18/5 }}} means that {{{10y = 18(y-4) }}}


So, {{{10y = 18y - 72}}}
{{{-8y = -72}}}
{{{y= 9}}}


This value of y does NOT make any denominators zero, so there are no extraneous roots.  However, it's easy to check by substituting y=9 in the original equation:
{{{(2y)/( y - 4) - 3/ 5 = 3}}}
{{{(2*9)/( 9 - 4) - 3/ 5 = 3}}}
{{{18/5 - 3/5 = 3}}}
{{{15/5 = 3}}}


It checks!!


R^2 at SCC