8.1.3 Adding and Subtracting Rational Expressions - Worksheet
Example 1: Add or subtract. Identify any x -values for which the expression is undefined. 1. x x x x 2 3 4 1 3 4 4 1 − − + + − 2. − + − + + x x x x 3 4 4 5 5 3 4 5 3. − − − x x 4 3 2 5
+ − 4 3 2 5 x x
Example 2: Find the least common multiple for each pair. 4. 4 x 2 y 3 and 16 x 4 y
5. x 2 − 25 and x 2 + 10 x + 25
Example 3: Add. Identify any x -values for which the expression is undefined. 6. x x x x 3 2 6 2 3 2 1 − + + − − 7. x x x x 4 5 12 4 3 1 3 1 − + + − +
8. x x 2
x 2 1 3 x − +
3 4 9 − −
+
Example 4: Subtract. Identify any x -values for which the expression is undefined. 9. x x x x 3 5 2 5 2 5 3 1 − − − − + 10. x x x 2 8 16 3 4 2 + − − − 11.
x x x 2
x x
2 4 3
1 3
+ + +
+ +
−
Example 5: Simplify. Assume that all expressions are defined. 12. x x x x 2 3 2 4 3 4 2 − − − − 13. x x x x 3 7 4 5 6 1 5 6 − + − −
14. x x x x 2 1 2 2 + +
Example 6: 15. Yvette ran at an average speed of 6.20 ft/s during the first two laps of a race and an average speed of 7.75 ft/s during the second two laps of a race. What was Yvette’s average speed for the entire race? Round to the nearest tenth.
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