Remember that if any solutions would also make any of the original denominators zero, those solution(s) must be excluded from the final answer set.
So, 3(x-3) -5x = 3× 5 = 15
Using the distributive law,
3x -9 -5x = 15
Combining like terms,
-2x -9 = 15
Adding 9 to both sides:
-2x = 24
Dividing both sides by the coefficient of x:
x = -12
Two of the three original denominators would be zero if x were zero. Since the only solution found is x = -12, no found solutions need to be excluded from our final solution set.
Finally, checking our answer "suspect":
( (-12) - 3 ) / (-12) - (5/3) = (-15)/(-12) -(5/3)
= (15/12) -(20/12) = (-5/12) = (5/(-12))
So, this verifies that x = -12 is the one and only valid solution to the original equation, and hence "the suspect is truly guilty".
