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Factorization of Fractions

You can simplify fractions through factorization to make calculations—and your life—easier.

Example 1

Simplify the fraction $\frac{2 x + 4}{x + 2}$

Here you should factorize the numerator and denominator separately. If you find the same factors above and below the fraction bar, they can be canceled. The numerator is

2 x + 4 = 2 \times x + 2 \times 2 = 2 (x + 2)

The denominator is just $x + 2$ . You can now see that $x + 2$ is a common factor for the numerator and denominator, and you therefore have that

\frac{2 x + 4}{x + 2} = \frac{2 (x+2)}{x+2} = 2

Here is an example with powers:

Example 2

Simplify the fraction $\frac{2 b^{3} + 4 b^{6}}{12 + 24 b^{3}}$

You factorize the numerator first and get

2 b^{3} + 4 b^{6} = 2 b^{3} (1 + 2 b^{3})

Then you factorize the denominator and get

12 + 24 b^{3} = 12 (1 + 2 b^{3})

You can see that $1 + 2 b^{3}$ is a common factor in the numerator and denominator, and can therefore be canceled. You get

\begin{array}{l} \frac{2 b^{3} + 4 b^{6}}{12 + 24 b^{3}} & = \frac{2 b^{3} (1+2b^{3})}{12 (1+2b^{3})} \\ = \frac{2 b^{3}}{12} \\ = \frac{b^{3}}{6} . \end{array}

\frac{2 b^{3} + 4 b^{6}}{12 + 24 b^{3}} = \frac{2 b^{3} (1+2b^{3})}{12 (1+2b^{3})} = \frac{2 b^{3}}{12} = \frac{b^{3}}{6}

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Factorization of Expressions

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