Question 707909
If the problem is {{{(x(2x+1))/(x-4) = 36/(x-4)}}}, then you can multiply both sides by x-4 to get {{{x(2x+1) = 36}}}


If you solve that for x, you will get 4, -9/2 ... BUT...these are the solutions to {{{x(2x+1) = 36}}} and NOT the original equation.


This is why you must check any and all possible answers you get in the original equation.


Notice that if x = 4, then x - 4 is equal to zero. But x-4 is a denominator and if that is zero, then you have a division by zero error. To avoid this division by zero error, you make the restriction that {{{x<>4}}}


So x = 4 is NOT a solution


This just leaves the only solution to be -9/2