Evaluate Rational Expressions

Find the excluded value(s).

• n = 0

• n = 24

• n = -24

• n can be any real number

Find the excluded value(s).

• v = 5

• v = 10

• v = -25

• v = -5

State the excluded (undefined) values for the given expression.

• 8, -10

• 8, 9

• -8, 10

• -8, -9

Simplify. 

• (m+6)/(m-3)

• 7/(m-3)

• 7(m+6)

• (m-3)

Simplify. 

• (x+6)/(x+4)

• (x+6)(x+4)

• (x+6)

• (x+6)/(x-5)

Evaluate:

• 2

• 4

• 16

• 64

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

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

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