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Simplifying fractions

A fraction with polynomials is simplified by factorising the numerator and the denominator and cancelling common factors. You can never cancel terms. In $\dfrac{x + 2}{x}$ the $x$ is a term in the numerator, so the fraction becomes $1 + \dfrac{2}{x}$ and not $2$. The value where the cancelled factor is zero must be excluded, because the original fraction is not defined there.

Symbols

Example

$\frac{x^2 - 4}{x - 2} = x + 2$ for $x \ne 2$. For $x = 5$: $\frac{21}{3} = 7$ and $5 + 2 = 7$.

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Part of Mathematics 1T: Factorisation and polynomial division.