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Complex fractions

Complex fractions. Objective. Simplify complex fractions Lets Review fraction rules first…………. - 5. - 5. - 5. 3. Multiply. ·. 21. 21. 21. 4. 3. 3. - 5. 1. - 5. =. ·. ·. =. ·. =. 4. 4. 7. 4. 28. Multiplying Fractions. 1. 7. Multiply.

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Complex fractions

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  1. Complex fractions

  2. Objective • Simplify complex fractions • Lets Review fraction rules first…………..

  3. - 5 - 5 - 5 3 Multiply . · 21 21 21 4 3 3 - 5 1 - 5 = · · = · = 4 4 7 4 28 Multiplying Fractions 1 7

  4. Multiply Multiplying Rational Expressions • Factor all numerators and denominators completely. • Divide out common factors. • Multiply numerators together and multiply denominators together.

  5. - 2 - 2 - 2 - 2 5 5 Divide .   9 9 9 9 9 9 9 9 - 2 = · · = = 5 5 5 Dividing Two Fractions 1 1

  6. Divide Dividing Rational Expressions Invert the divisor (the second fraction) and multiply

  7. 5 5 2 2 Add . + + 12 12 12 12 7 = 12 Adding/Subtracting Fractions

  8. Subtract Common Denominators • Add or subtract the numerators. • Place the sum or difference of the numerators found in step 1 over the common denominator. • Simplify the fraction if possible.

  9. a.) Add Common Denominators Example:

  10. b.) Subtract Common Denominators Example:

  11. Unlike Denominators • Determine the LCD. • Rewrite each fraction as an equivalent fraction with the LCD. • Add or subtract the numerators while maintaining the LCD. • When possible, factor the remaining numerator and simplify the fraction.

  12. a.) Unlike Denominators Example: The LCD is w(w+2).

  13. b.) This cannot be factored any further. Unlike Denominators Example: The LCD is 12x(x – 1).

  14. Complex Fractions

  15. Simplifying Complex Fractions A complex fractionis one that has a fraction in its numerator or its denominator or in both the numerator and denominator. Example:

  16. So how can we simplify them? • Remember, fractions are just division problems. • We can rewrite the complex fraction as a division problem with two fractions. • This division problem then changes to multiplication by the reciprocal.

  17. Simplifying Complex Fractions Rule • Any complex fraction Where b ≠ 0, c ≠ 0, and d ≠ 0, may be expressed as:

  18. What if we have mixed numbers in the complex fraction? • If we have mixed numbers, we treat it as an addition problem with unlike denominators. • We want to be working with two fractions, so make sure the numerator is one fraction, and the denominator is one fraction • Now we can rewrite the complex fraction as a division of two fractions

  19. Example

  20. Try on your own…

  21. What about complex rational expression? • Treat the complex rational expression as a division problem • Add any rational expressions to form rational expressions in the numerator and denominator • Factor • Simplify • “Bad” values

  22. Ex. 2: Simplify ← The LCD is xy for both the numerator and the denominator. ← Add to simplify the numerator and subtract to simplify the denominator. ← Multiply the numerator by the reciprocal of the denominator.

  23. Ex. 2: Simplify ← Eliminate common factors.

  24. Example

  25. Example

  26. Try on your own

  27. One more for you

  28. Ex. 3: Simplify ← The LCD of the numerator is x + 4, and the LCD of the denominator is x – 3.

  29. Ex. 3: Simplify ← FOIL the top and don’t forget to subtract the 1 and add the 48 on the bottom.

  30. Ex. 3: Simplify ← Simplify by subtracting the 1 in the numerator and adding the 48 in the denominator.

  31. Ex. 3: Simplify ← Multiply by the reciprocal. x2 + 8x +15 is a common factor that can be eliminated.

  32. Ex. 3: Simplify ← Simplify

  33. Model Problems

  34. Homework • Practice Sheet

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