Example

Finding the Sum x3+23\frac{x}{3} + \frac{2}{3}

Apply the common-denominator addition rule to add two fractions that share the denominator 33, one of which contains a variable:

x3+23\frac{x}{3} + \frac{2}{3}

Because the denominators are already the same, add the numerators and place the result over the common denominator:

x+23\frac{x + 2}{3}

The expression x+23\frac{x + 2}{3} cannot be simplified further because the numerator x+2x + 2 and the denominator 33 share no common factor. This example illustrates that the fraction addition rule ac+bc=a+bc\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c} applies in exactly the same way when one or both numerators are algebraic expressions rather than plain numbers.

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Updated 2026-04-21

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Ch.1 Foundations - Elementary Algebra @ OpenStax

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