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9.5 Addition, Subtraction, and Complex Fractions

9.5 Addition, Subtraction, and Complex Fractions. Adding and Subtracting. Steps for Adding and Subtracting with like denominators Add or Subtract the Numerators Place results over Common Denominator Simplify (If necessary). Examples. Adding and Subtracting.

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9.5 Addition, Subtraction, and Complex Fractions

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  1. 9.5 Addition, Subtraction, and Complex Fractions

  2. Adding and Subtracting • Steps for Adding and Subtracting with like denominators • Add or Subtract the Numerators • Place results over Common Denominator • Simplify (If necessary)

  3. Examples

  4. Adding and Subtracting • Steps for Adding and Subtracting with Unlike Denominators • Find the least common denominator • Rewrite each expression as equivalent rational expressions using LCD • Continue with steps for like denominators

  5. Examples:

  6. Examples:

  7. Examples: • Given the following rational functions: • Graph each function. For what values of x is y1 a maximum? y2? • Graph a model hat shows the sum of the functions. For what value of x is this function a maximum?

  8. Complex Fractions • Complex fraction: is a fraction that contains a fraction in its numerator or denominator. • To Solve Complex Fractions: • Write its numerator and denominator as single fractions • Then divide by multiplying by the reciprocal of the denominator

  9. Examples:

  10. Examples:

  11. Example • The focal length f(in centimeters) of a curved mirror is: where d0 is the image’s distance from the mirror. Simplify the complex fraction.

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