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Rational Expressions Homework -- Sample Test: Rational Expressions

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

Summary: A sample test covering rational expressions.

Exercise 1

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

Exercise 2

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

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

Exercise 3

4x39xx23x10× 2x220x+506x29x4x39xx23x10 size 12{ { {4x rSup { size 8{3} } - 9x} over {x rSup { size 8{2} } - 3x - "10"} } } {}×2x220x+506x29x size 12{ { {2x rSup { size 8{2} } - "20"x+"50"} over {6x rSup { size 8{2} } - 9x} } } {}

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

Exercise 4

1 x x - 1 x 2 1 x x - 1 x 2

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

Exercise 5

6x 3 5x 2 5x + 34 2x + 3 6x 3 5x 2 5x + 34 2x + 3 size 12{ { {6x rSup { size 8{3} } - 5x rSup { size 8{2} } - 5x+"34"} over {2x+3} } } {}

  • a. Solve by long division.
  • b. Check your answer (show your work!!!).

Exercise 6

If f ( x ) = x 2 f(x)= x 2 , find f(x+h)f(x)hf(x+h)f(x)h size 12{ { {f \( x+h \) - f \( x \) } over {h} } } {}. Simplify as much as possible.

Exercise 7

x12x1= x+77x+4x12x1 size 12{ { {x - 1} over {2x - 1} } } {}=x+77x+4 size 12{ { {x+7} over {7x+4} } } {}

  • a. Solve for xx.
  • b. Test one of your answers and show that it works in the original expression. (No credit unless you show your work!)

Extra credit:

I am thinking of two numbers, xx and y y, that have this curious property: their sum is the same as their product. (Sum means “add them”; product means “multiply them.”)

  • a. Can you find any such pairs?
  • b. To generalize: if one of my numbers is xx, can you find a general formula that will always give me the other one?
  • c. Is there any number xx that has no possible yy to work with?

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