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Cogito

Integrated Math 3 · Chapter 2 · Lesson 2

Practice Worksheet

Operations With Rational Expressions

Fractions, with polynomials inside.

12 problems · about 21 minutes · A-APR.D.7

NameDate

Figure — use these to answer the problems

The rules for rational expressions are the fraction rules. Compare these two and the parallel is exact.
2/3
3/4
012/33/4

2/3 is less than 3/4.

Left numerator2
Left denominator3
Right numerator3
Right denominator4
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. For 1 ÷ (x − 9), which value of x is excluded?

    Answer

  2. What may be cancelled from a fraction?

    • Whole factors only.
    • Any matching symbols.

  3. For 1 ÷ (x − 5), which x is excluded?

    Answer

  4. For 1 ÷ (x + 4), which x is excluded?

    Answer

  5. Can the x values in (x + 3) ÷ (x + 5) be cancelled? 1 yes, 0 no.

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. To divide by a fraction, what do you multiply by? 1 the same, 2 the reciprocal.

    Answer

  2. (x² − 4) ÷ (x − 2) simplifies to x + k. What is k?

    Answer

  3. (x² − 25) ÷ (x + 5) simplifies to x − k. What is k?

    Answer

Stretch Yourself

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

4 problems

  1. Put the addition process in order.

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

    • Factor every denominator.
    • Build the least common denominator.
    • Rewrite each fraction over it.
    • Add the numerators and simplify.

  2. (x² − 36) ÷ (x − 6) simplifies to x + k. What is k?

    Answer

  3. The Restriction

    For (x − 3) ÷ (x + 2), which value of x is excluded?

    Answer

  4. The Cancel

    In (x² − 9) ÷ (x² + 5x + 6), which factor cancels? Enter 3 for (x + 3).

    Answer