Algebra 2 / Unit 6: Rational Functions
6.3 Adding and Subtracting Rational Expressions
Notes
You need a common denominator, just like with number fractions.
- Factor each denominator, then build the least common denominator (LCD).
- Rewrite each fraction over the LCD, then add or subtract the numerators. Keep the denominator.
- When subtracting, put the second numerator in parentheses.
- Example: $\displaystyle \frac{2}{x} + \frac{3}{x + 1} = \frac{2(x + 1) + 3x}{x(x + 1)} = \frac{5x + 2}{x(x + 1)}$.
Practice
Add $\displaystyle \frac{3}{x} + \frac{2}{x + 1}$.
$\displaystyle \frac{3(x + 1) + 2x}{x(x + 1)} = \frac{5x + 3}{x(x + 1)}$.
Simplify $\displaystyle \frac{x}{x - 2} - \frac{2}{x - 2}$.
$\displaystyle \frac{x - 2}{x - 2} = 1$ wherever it is defined.
Add $\displaystyle \frac{1}{x^2 - 4} + \frac{1}{x + 2}$.
LCD is $(x - 2)(x + 2)$: $\displaystyle \frac{1 + (x - 2)}{x^2 - 4} = \frac{x - 1}{x^2 - 4}$.
Ready for more? Take the Unit 6 test.