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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 2x + 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

2x + 4 = 2 × x + 2 × 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

2x + 4 x + 2 = 2(x + 2) x + 2 = 2

Here is an example with powers:

Example 2

Simplify the fraction 2b3 + 4b6 12 + 24b3

You factorize the numerator first and get

2b3 + 4b6 = 2b3 (1 + 2b3)

Then you factorize the denominator and get

12 + 24b3 = 12 (1 + 2b3)

You can see that 1 + 2b3 is a common factor in the numerator and denominator, and can therefore be canceled. You get

2b3 + 4b6 12 + 24b3 = 2b3(1 + 2b3) 12(1 + 2b3) = 2b3 12 = b3 6 .

2b3 + 4b6 12 + 24b3 = 2b3(1 + 2b3) 12(1 + 2b3) = 2b3 12 = b3 6

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