Addition and Subtraction of Algebraic Fractions - SS2 Mathematics Lesson Note
These operations involving algebraic fractions are solved much the same way as normal fractions.
Example 1 Simplify the following:
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\(\frac{2a}{15} + \frac{7a}{15}\)
\(\frac{7}{x - 2} - \frac{5 + x}{x - 2}\)
\(\frac{s^{2}}{{9r}^{2}} - \frac{s^{3}}{{12r}^{3}}\)
Solution
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\(\frac{2a}{15} + \frac{7a}{15}\)
\[\frac{2a + 7a}{15} = \ \frac{9a}{15}\]
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\(\frac{7}{x - 2} - \frac{5 + x}{x - 2}\)
\[\frac{7 - (5 + x)}{x - 2}\]
\[\frac{7 - 5 - x}{x - 2} = \ \frac{2 - x}{x - 2}\]
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\(\frac{s^{2}}{{9r}^{2}} - \frac{s^{3}}{{12r}^{3}}\)
\[= \ \frac{{4rs}^{2} - 3s^{3}}{{36r}^{3}}\]