In mathematics, the method of clearing denominators, also called clearing fractions, is a technique for simplifying an equation equating two expressions that each are a sum of rational expressions – which includes simple fractions.
But the same substitution applied to the original equation results in x/6 + 0/0 = 1, which is mathematically meaningless.
This means that each Qi is a factor of D, so D = RiQi for some expression Ri that is not a fraction.
So we have now Provided that D does not assume the value 0, the latter equation is equivalent with in which the denominators have vanished.
As shown by the provisos, care has to be taken not to introduce zeros of D – viewed as a function of the unknowns of the equation – as spurious solutions.