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Rational Equations

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

Summary: Practice exercises on rational equations.

Exercise 1

Suppose I tell you that x36=1536x36=1536 size 12{ { {x} over {"36"} } = { {"15"} over {"36"} } } {}. What are all the values x x can take that make this statement true?

OK, that was easy, wasn’t it? So the moral of that story is: rational equations are easy to solve, if they have a common denominator. If they don’t, of course, you just get one!

Exercise 2

Now suppose I tell you that x18=1536x18=1536 size 12{ { {x} over {"18"} } = { {"15"} over {"36"} } } {}. What are all the values xx can take that make this statement true?

Hey, x x came out being a fraction. Can he do that?

Umm, yeah.

OK, one more pretty easy one.

Exercise 3

x 2 + 2 21 = 9 7 x 2 + 2 21 = 9 7 size 12{ { {x rSup { size 8{2} } +2} over {"21"} } = { {9} over {7} } } {}

Did you get only one answer? Then look again—this one has two!

Once you are that far, you’ve got the general idea—get a common denominator, and then set the numerators equal. So let’s really get into it now…

Exercise 4

x + 2 x + 3 = x + 5 x + 4 x + 2 x + 3 = x + 5 x + 4 size 12{ { {x+2} over {x+3} } = { {x+5} over {x+4} } } {}

Exercise 5

2x + 6 x + 3 = x + 5 2x + 7 2x + 6 x + 3 = x + 5 2x + 7 size 12{ { {2x+6} over {x+3} } = { {x+5} over {2x+7} } } {}

Exercise 6

x+32x−3=x−5x−4x+32x−3 size 12{ { {x+3} over {2x - 3} } } {}=x−5x−4 size 12{ { {x - 5} over {x - 4} } } {}

  • a. Solve. You should end up with two answers.
  • b. Check both answers by plugging them into the original equation.

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