how to solve equation involving rational algebraic expression

Question

find the equation involving rational algebraic expression 1/x-4 - 4/x2-4x=0

Answer 1

1/(x-4)-4/(x²-4x)=0, multiply through by x²-4x:

x-4=0, x=4 appears to be the solution. However, if x=4 both fractions are indeterminate, therefore there is no solution. In other words, there is no value of x for which the given equation is true (trick question!).