Lesson 11 Simplifying Rational expressions

We will simplify rational expressions and state their restrictions.
I will summarize how to simplify rational expressions and determine their restrictions.
TEKs 2A.7F

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​Lesson 11 Simplifying Rational Expressions

Dropdown

The largest degree of the numerator is ​

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, the largest degree of the denominator is​

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. Therefore, N​

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D, and our horizontal asymptote is​

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Definition and review

If we do not state the restrictions then it is NOT the same function.

Multiple Choice

TRUE or FALSE:

$$\frac{\left(x-3\right)}{\left(x-3\right)\left(x+2\right)}$$ is equal to $$\frac{1}{\left(x+2\right)}$$

• True they are exactly the same thing.

• False, they are completely different because the second expression did not state the restrictions.

Desmos.com, graph and click the intersections with the x-axis.

Let's work these examples together

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Try these on your own.

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Multiple Choice

The Simplest forms for Example 3 and Example 4 is: (Pay close attention to your answer choices..)

• Ex 3: $$-\frac{\left(x-4\right)}{\left(x+3\right)};\ x\ne-2$$

  Ex 4: $$5\left(x+1\right);\ x\ne1$$

• Ex 3: $$-\frac{\left(x+4\right)}{\left(x-3\right)};\ x\ne2,\ 3$$

  Ex 4: $$5\left(x+1\right);\ x\ne1$$

• Ex 3: $$\frac{\left(x+4\right)}{\left(x+3\right)};\ x\ne-2$$

  Ex 4: $$5\left(x+1\right);\ x\ne-1$$

• Ex 3: $$\frac{\left(x-4\right)}{\left(x+3\right)};\ x\ne-2$$

  Ex 4: $$5\left(x+1\right);\ x\ne1$$

Look for any GCF to factor out first - both of these examples have at least one

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Dropdown

The restrictions for the simplified form of Example 5 is/are: ​ ​

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and the restrictions for Example 6 is/are:​

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Last set of examples!

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Math Response

For the very last example (8), what is the simplest form? List only the form, we are assuming the restrictions are correct here.

Type answer here

Correct Answer: 2x

Deg^°

Rad

Poll

Rate your understanding of the topic for today.

• 5 - Highest understanding

• 4 - Mostly Confident

• 3 - Not as confident want some more practice

• 2 - Need more practice to raise my confidence

• 1 - not confident at all and feeling a little lost

Open Ended

Summary below.