SOLUTION: Which numbers cannot be used in place of the variable in each rational expression? 18. 2y + 1 y2 – y -6

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Question 168684: Which numbers cannot be used in place of the variable in each rational expression?
18. 2y + 1
y2 – y -6
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%282y%2B1%29%2F%28y%5E2-y-6%29 Start with the given expression


y%5E2-y-6=0 Set the denominator equal to zero. Remember, dividing by 0 is undefined. So if we find values of y that make the denominator zero, then they cannot be used in place of the variable


%28y-3%29%28y%2B2%29=0 Factor the left side (note: if you need help with factoring, check out this solver)




Now set each factor equal to zero:

y-3=0 or y%2B2=0

y=3 or y=-2 Now solve for y in each case


So our solutions are y=3 or y=-2



Since y=-2 and y=3 make the denominator equal to zero, this means these values CANNOT be used in the rational expression


So y=-2 and y=3 cannot be used.