Question 442607
{{{x/(x-6)-6/(x+6)=72/(x^2-36)}}}

Notice {{{x^2-36 =  (x+6)(x-6)}}}

Then {{{x/(x-6) - 6/(x+6) = 72/((x+6)(x-6))}}}

What will our common denominator be between these three denominators? (x+6)(x-6), right.

So we can rewrite {{{x/(x-6) = x(x+6)/(x-6)(x+6)}}}

Similarly we can rewrite {{{6/(x+6) = 6(x-6)/(x+6)(x-6)}}}

So now we have {{{(x*(x+6) - 6(x-6))/(x+6)(x-6) = 72/(x+6)(x-6)}}}

Now we can solve solely for the numerator.

{{{x^2 + 6x - 6x +36 = x^2 + 36 = 72}}}
{{{x^2 = 36}}}

So {{{x = 6}}} and {{{x=-6}}}

But wait! We need to check if these solutions are extraneous. A solution is extraneous if it makes the expression undefined. (AKA: division by 0)

Our denominator is (x+6)(x-6), so it is 0 when x =6 or x=-6.

So both x=6 and x=-6 are EXTRANEOUS! 

Thus there is no solution.