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A student says that you can reduce the 8 and the x from the following expression: 2x-8 /  x^2 -6 + 8  and get 2/x-6. Why is this incorrect?

 Oct 18, 2018
 #1
avatar+98090 
+1

1  is in the domain of both functions....so....subbing any number in the domain into both fumctions should make them equal

 

So

 

[ 2 (1) - 8 ] / [ 1^2 - 6 - 8 ]   =  ???     2 / [ 1 - 6]

 

[ - 5 ] / [ - 13 ]  =  ???  2 / -5

 

5/13  =  ???  - 2/5

 

Not true...so......these functions are not equal

 

 

cool cool cool

 Oct 18, 2018
 #2
avatar+17283 
+2

Another method:

 

2(x-4) /( (x-2)(x-4) )

 

= 2 / (x-2)      NOT   2/(x-6)

 Oct 18, 2018

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