We are given four options, each including a fraction with the variable w. Among these options we will find the one that is undefined when w=3. Recall that if the denominator of a fraction is zero, the expression is undefined. Let's now substitute w= 3 into each fraction and solve.
Option
Fraction
Substitution
Result
A
w-3/w+1
3-3/3+1=0/4
0
B
w^2-3w/3w
3^2-3( 3)/3( 3)=0/9
0
C
w+1/w^2-3w
3+1/3^2-3( 3)=4/0
Undefined
D
3w/3w^2
3( 3)/3( 3)^2=9/27
1/3
As we can see from the table, the denominator of the fraction in option C becomes 0 when w is equal to 3. This means that this fraction is undefined when w=3. To see a step-by-step explanation for these calculations, please see the bottom of this solution.
Showing Our Work
Substitution
Let's explain the calculations in the substitutions step-by-step. We will start with the option A and substitute w=3 into the fraction w-3w+1.
Notice that the denominator of the fraction in option C is 0. It means that it is undefined when w=3. Finally, let's substitute w=3 into the fraction in option D.
