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Homework: Rational Expressions

Module by: Kenny M. Felder. E-mail the author

Summary: Homework exercises for rational expressions.

Exercise 1

x2−6x+5x2−16×x2+8x+16x2−7x+10x2−6x+5x2−16 size 12{ { {x rSup { size 8{2} } - 6x+5} over {x rSup { size 8{2} } - "16"} } } {}×x2+8x+16x2−7x+10 size 12{ { {x rSup { size 8{2} } +8x+"16"} over {x rSup { size 8{2} } - 7x+"10"} } } {}

  • a. Simplify
  • b. What values of xx are not allowed in the original expression?
  • c. What values of x x are not allowed in your simplified expression?

Exercise 2

2 x 2 + 7 x + 3 x 3 + 4 x x 2 + x - 6 3 x 2 x 2 + 7 x + 3 x 3 + 4 x x 2 + x - 6 3 x

  • a. Simplify
  • b. What values of x x are not allowed in the original expression?
  • c. What values of x x are not allowed in your simplified expression?

Exercise 3

1 x − 1 − 1 x + 1 1 x − 1 − 1 x + 1 size 12{ { {1} over {x - 1} } - { {1} over {x+1} } } {}

  • a. Simplify
  • b. What values of x x are not allowed in the original expression?
  • c. What values of x x are not allowed in your simplified expression?
  • d. Test your answer by choosing an x x value and plugging it into the original expression, and your simplified expression. Do they yield the same answer?

Exercise 4

x − 3 x 2 + 9x + 20 − x − 4 x 2 + 8x + 15 x − 3 x 2 + 9x + 20 − x − 4 x 2 + 8x + 15 size 12{ { {x - 3} over {x rSup { size 8{2} } +9x+"20"} } - { {x - 4} over {x rSup { size 8{2} } +8x+"15"} } } {}

  • a. Simplify
  • b. What values of x x are not allowed in the original expression?
  • c. What values of x x are not allowed in your simplified expression?

Exercise 5

x + 1 4x 2 − 9 + 4x 6x 2 − 9x x + 1 4x 2 − 9 + 4x 6x 2 − 9x size 12{ { {x+1} over {4x rSup { size 8{2} } - 9} } + { {4x} over {6x rSup { size 8{2} } - 9x} } } {}

  • a. Simplify.
  • b. Test your answer by choosing an x x value and plugging it into the original expression, and your simplified expression. Do they yield the same answer?

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