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Rational Expressions

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

Summary: Practice exercises on rational exercises.

Exercise 1

1x+ 1y1x size 12{ { {1} over {x} } } {}+1y size 12{ { {1} over {y} } } {}

  • a. Add
  • b. Check your answer by plugging x = 2 x=2 and y = 4 y=4 into both my original expression, and your simplified expression. Do not use calculators or decimals.

Exercise 2

1x– 1y=1x size 12{ { {1} over {x} } } {}–1y size 12{ { {1} over {y} } } {}=

Exercise 3

1x1y=1x1y size 12{ left ( { {1} over {x} } right ) left ( { {1} over {y} } right )} {}=

Exercise 4

1 x 1 y = 1 x 1 y =

Exercise 5

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

  • a. Simplify
  • b. Check your answer by plugging x = 3 x=3 into both my original expression, and your simplified expression. Do not use calculators or decimals.
  • c. Are there any x-values for which the new expression does not equal the old expression?

Exercise 6

2x2−9- 4x2+2x−15=2x2−9 size 12{ { {2} over {x rSup { size 8{2} } - 9} } } {}-4x2+2x−15 size 12{ { {4} over {x rSup { size 8{2} } +2x - "15"} } } {}=

Exercise 7

4x2−25x2+2x+1×x2+4x+32x2+x−154x2−25x2+2x+1 size 12{ { {4x rSup { size 8{2} } - "25"} over {x rSup { size 8{2} } +2x+1} } } {}×x2+4x+32x2+x−15 size 12{ { {x rSup { size 8{2} } +4x+3} over {2x rSup { size 8{2} } +x - "15"} } } {}

  • a. Multiply.
  • b. Check your answer by plugging x = –2 x=–2 into both my original expression, and your simplified expression. (If they don’t come out the same, you did something wrong!)
  • c. Are there any x-values for which the new expression does not equal the old expression?

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