### Algebra: Adding and subtracting fractions

### Fractions

Fractions with variables

Variables can occur in both the #\orange{\text{numerator}}# as well as the #\blue{\text{denominator }}# of fraction. Just like a fraction with numbers, the #\blue{\text{denominator }}# cannot be equal to #0#. Therefore, we cannot enter numbers for which the denominator is equal to #0#. Most of the time, we will not mention this explicitly, but will assume this value is not entered. |
\[\frac{\orange{x+3}}{\blue{x-5}} \] \[\frac{\orange{x}}{\blue{x^2-1}} \] |

#-{{1}\over{3}}#

This result can be found by replacing #x# with #3# everywhere:

\[\displaystyle {{3}\over{-3^2-3+3}}= -{{1}\over{3}}\tiny.\]

This result can be found by replacing #x# with #3# everywhere:

\[\displaystyle {{3}\over{-3^2-3+3}}= -{{1}\over{3}}\tiny.\]

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