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How do you simplify #(4-2(x-1))/(x^2-6x+9)#?

Answer 1

Nathan Axel

#(-2)/(x-3)#

#(4-2(x-1))/(x^2-6x+9)#

#=(4-2x+2)/(x^2-6x+9)#

#=(-2x+6)/(x^2-6x+9#

#=(-2(x-3))/((x-3)(x-3))#

#=(-2color(red)cancelcolor(black)((x-3)))/(color(red)cancelcolor(black)((x-3))(x-3))#

#=(-2)/(x-3)#

Note: #(4-2(x-1))/(x^2-6x+9)# is not the same as #((4-2)(x-1))/(x^2-6x+9)#

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Answer 2

Avery Alexander

To simplify the expression (4-2(x-1))/(x^2-6x+9), we can start by simplifying the numerator and the denominator separately.

First, let's simplify the numerator: 4 - 2(x-1) = 4 - 2x + 2 = 6 - 2x

Next, let's simplify the denominator: x^2 - 6x + 9 is a perfect square trinomial, which can be factored as (x-3)^2.

Now, we can rewrite the expression as: (6 - 2x)/(x-3)^2

And that is the simplified form of the expression (4-2(x-1))/(x^2-6x+9).

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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.