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The shortcut for simplifying complex fractions applies the fundamental principle of fractions.

An improper algebraic fraction is one in which the denominator has higher degree than the numerator.

If the remainder is zero in polynomial division $\dfrac{p(x)}{q(x)} \text{,}$ the numerator $p(x)$ can be factored.

If the divisor in polynomial division is a binomial, we use a process like long division.