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Cogito

Algebra 2 · Chapter 4 · Lesson 2

Practice Worksheet

Adding and Simplifying Rational Expressions

Common denominators, with letters.

11 problems · about 23 minutes · A-APR.D.7

NameDate

Figure — use these to answer the problems

A rational function, with the asymptote its denominator creates.

y = 1/x + 0

a1

Figure 1

Warm Up

Straightforward practice. Get the method working first.

4 problems

(x² − 36)/(x − 6) simplifies to x + what?
Answer
(x² − 25)/(x − 5) simplifies to x + what?
Answer
Can the x values in (x + 2)/(x + 7) cancel? 1 for yes, 0 for no.
Answer
(x² − 1)/(x + 1) simplifies to x − what?
Answer

Build It Up

The same ideas with more to keep track of.

3 problems

1/x + 1/x. What is the numerator over x?
Answer
For 5/(x − 6), which x is excluded?
Answer
(3/x) × (x/4). Result as a decimal?
Answer

Stretch Yourself

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

4 problems

8
Order the steps for simplifying a rational expression.
Write 1 to 3 in the boxes to put these in order.
- Factor the numerator and denominator
- Note the excluded values
- Cancel shared factors
Does cancelling restore the excluded value? 1 for yes, 0 for no.
Answer
Simplifying
(x² − 4)/(x − 2) simplifies to x + what?
Answer
The Excluded Value
For that expression, which x is excluded?
Answer