When solving a rational equation, why is it necessary to perform a check?

Answer 1

If you mean something like
x^2 = 25
then x = +5 or x = -5
only one of the two solutions may solve your original problem. Therefore you try them both in the original problem that led to x^2 = 25 to see if one or the other or both works.

Answer 2

Basically to see if the value found for x will yield the same answer on both sides of the equation.