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.
For when we substitute y = 0 and z = 0 in the last equation, both sides simplify to 0, so we get 0 = 0, a mathematical truth.
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.
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.