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Mastering Rational Expressions: Simplifying, Multiplying, Factoring, and more

Learn how to simplify, multiply, factor, find LCD, and solve equations with rational expressions step by step in this comprehensive teaching guide.

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Mastering Rational Expressions: Simplifying, Multiplying, Factoring, and more

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  1. Chapter R.5 Rational Expressions

  2. Teaching Example 1 Simplify each expression. Solution

  3. Teaching Example 1 (continued)

  4. Teaching Example 2 Multiply and simplify. Solution

  5. Teaching Example 3 Multiply. Solution

  6. Multiply by Teaching Example 4 Divide and simplify. Solution “Invert and multiply.”

  7. Teaching Example 4 (continued) “Invert and multiply.” Factor numerator and denominator. Simplify.

  8. Teaching Example 5 Find the least common multiple for each pair of expressions. Solution (a) Factor each monomial completely.

  9. Teaching Example 5 (continued) (b) Factor each polynomial completely.

  10. Teaching Example 6 Find the least common denominator (LCD) for Solution From Teaching Example 5(b), Thus, the LCD is (x + 1)(x + 7)(x − 7).

  11. Teaching Example 7 Simplify Solution

  12. Teaching Example 8 Simplify Solution

  13. Teaching Example 9 Add and simplify. Solution

  14. Teaching Example 9 (continued) The denominators are different, so find the LCD. LCD = (x − 4)(x + 4) Change each fraction to the common denominator.

  15. Teaching Example 9 (continued)

  16. Teaching Example 10 Subtract and simplify Solution The LCD is 2x(x + 1).

  17. Teaching Example 11 Clear fractions from the equation and solve. Solution Multiply both sides of the equation by the LCD,x(x − 4)(x + 4).

  18. Teaching Example 11 (continued)

  19. Teaching Example 12 Simplify Solution Multiply the numerator and denominator by the LCD, x(x − 2).

  20. Teaching Example 12 (cont) Distribute and simplify.

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