### Algebra: Adding and subtracting fractions

### Fraction decomposition

Until now we have taken fractions together to compose one fraction, but sometimes it can help to decompose fractions.

Fraction decomposition

A fraction with multiple terms in the numerator can be decomposed by using the terms in the numerator as the numerator of a new fraction. The denominator does not change. \[\frac{{\blue a+ \green b}}{{\purple c}}=\frac{{\blue a}}{{\purple c}}+ \frac{{\green b}}{{\purple c}}\] |
\[\begin{array}{rcl} \dfrac{\blue{x^2}+\green{5 \cdot x}}{\purple{x \cdot y}}&=&\dfrac{\blue{x^2}}{\purple{x \cdot y}}+ \dfrac{\green{5 \cdot x}}{\purple{x \cdot y}} \\ &=& \dfrac{{x}}{{y}}+ \dfrac{{5}}{{y}} \end{array}\] |

#{{-2\cdot b-2}\over{-4\cdot b-2}}=# #-{{2\cdot b}\over{-4\cdot b-2}}-{{2}\over{-4\cdot b-2}}#

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