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How do you simplify #(x-2)/(x^2-8x+12 )#?

Answer 1

#1/(x-6)#

First, factor the denominator completely.

#(x-2)/(x^2-8x+12)# #=(x-2)/((x-2)(x-6))# #=cancel(x-2)/(cancel((x-2))(x-6))# #color(blue)(=1/(x-6))#

WARNING: You can simplify this, however, take note that you have canceled out #(x-2)# in the denominator. If you are asked for the domain, make sure that #color(red)(x-2!=0)# or #color(red)(x!=2)#.

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Answer 2

Kennedy Adams

To simplify (x-2)/(x^2-8x+12), we can factor the denominator. The factored form of the denominator is (x-6)(x-2). Next, we can cancel out the common factor of (x-2) in the numerator and denominator. Therefore, the simplified form is 1/(x-6).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.