Question 2248
i am assuming that the first numerator is x-6 and not just 6...

{{{(x-6)/(x) - (x+6)/(x-6) = 6/x}}}

First thing...get rid of the fractions by multiplying everything by x(x-6):

{{{(x(x-6)(x-6))/(x) - (x(x-6)(x+6))/(x-6) = (6x(x-6))/x }}}

this gives...{{{(x-6)(x-6) - x(x+6) = 6(x-6)}}}

So, now, {{{x^2-12x+36 - x^2-6x = 6x-36}}}
-24x = -72
x=3

Always check your answer..put x=3 into the original and make sure that the Left side does equal the right side.

jon