Find Restrictions of Rational Expressions

When simplifying rational expressions, what is a restriction?

• A value of a variable that makes the expression mathematically illegal.

• A vertical asymptote

• A hole in the graph

• The negative or opposite of the denominator

• The negative or opposite of the numerator

I Do: How do we find the restrictions of a rational expression?

• We set the numerator equal to zero and solve for the variable

• We set the denominator equal to zero and solve for the variable

• We plug zero into the numerator and simplify

• We plug zero into the denominator and simplify

Simply the expression. State the restricted values.

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• Restricted Values: -4, -5

• Restricted Values: 2, -4

Simply the expression. State the restricted values.

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• Restricted values: 1, 2/5

• Restricted values: -1, 5/2

What is the domain restriction?

• A

• B

• C

• D

What are the restrictions of: \frac{1}{5y\ -\ 4}

Simply the expression. State the restricted values.

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• 
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• Restricted Values: 1, -3/2

• Restricted Values: -1, 3/2

Student 1 says that the restrictions of $\frac{9\left(d-4\right)}{\left(d-7\right)\left(d+8\right)}$ are $d\ne4$ , $d\ne7$ , and $d\ne-8$ . Is Student 1 correct? Why?

• Yes because d = 4, d = 7, and d = -8 all make the denominator equal to zero

• Yes because d = 4, d = 7, and d = -8 all make the expression evaluate to zero

• No because d = 4 does not make the denominator equal to zero

• No because d = 0 is also a restriction