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What is the sum of all values of y for which the expression (y + 6)/(y^2 - 4y + 4) is undefined?

 May 5, 2022
 #1
avatar+1366 
+2

For the equation to be undefined, the denominator must equal 0, because anything divided by 0 is undefined. 

 

Thus, we have the equation: \(y^2-4y+4=0\), where we have to solve for y.

 

To solve for y, use the quadratic formula: \(y = {-b \pm \sqrt{b^2-4ac} \over 2a}\) , because the quadratic is in the form \(ax^2+bx+c=0\)

 

Can you do it from here?

 May 5, 2022
 #2
avatar+122385 
+1

y^2 - 4y + 4  factors as    (y -2)^2

 

So

 

(y -2)^2 = 0

 

So  when y = 2, the denominator   = 0  and  the expression is undefined

 

cool cool cool

 May 5, 2022

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