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Cogito

Integrated Math 3 · Chapter 2 · Lesson 3

Practice Worksheet

Solving Rational Equations

Clearing the denominators, then checking.

12 problems · about 21 minutes · A-REI.A.2

NameDate

Figure — use these to answer the problems

The curve has no value at the asymptote. A solution landing there cannot be a real solution.
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y = 1/x + 0
  • Point(2, 0.50)
a1
Point on the curve2
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. 15 ÷ x = 5. What is x?

    Answer

  2. Why can extraneous solutions appear?

    • Multiplying by an expression that could be zero is not reversible.
    • They come from arithmetic mistakes.

  3. 12 ÷ x = 4. What is x?

    Answer

  4. 10 ÷ x = 5. What is x?

    Answer

  5. 1 ÷ (x − 3) = 1. What is x?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. A candidate makes a denominator zero. Is it valid? 1 yes, 0 no.

    Answer

  2. 8 ÷ (x + 1) = 2. What is x?

    Answer

  3. Is checking optional for rational equations? 1 yes, 0 no.

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

  1. Put the solving process in order.

    Write 1 to 4 in the boxes to put these in order.

    • Find the least common denominator.
    • Multiply every term by it.
    • Solve the resulting equation.
    • Check each answer in the original and reject any that break it.

  2. 20 ÷ x = 4. What is x?

    Answer

  3. The Rejection

    x ÷ (x − 2) = 2 ÷ (x − 2). How many valid solutions?

    Answer

  4. The Simple Case

    6 ÷ x = 3. What is x?

    Answer