Question 658796
how do you solve and check the rational equation of
{{{ 1/2x + (x-2)/2x = (x-2)/(2x+1) }}} 
{{{(x-1)/2x = (x-2)/(2x+1)}}}
cross=multiply
{{{2x(x-2)=(x-1)(2x+1)}}}
{{{2x^2-4x=2x^2-x-1}}}
3x=1
x=1/3
check:
plug x=1/3 into original equation:
{{{ 1/2x + (x-2)/2x = (x-2)/(2x+1) }}}
{{{(1/2*1/3)+(1/3-2)/(2*1/3)=(1/3-2)/(2*1/3+1)}}}
{{{1/(2/3)+(-5/3)/(2/3)=(-5/3)/(5/3)}}}
3/2-5/2=-1
-2/2=-1
-1=-1