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How do you simplify #(x^2-2x-3)/(x^2-7x+12)#?

Answer 1

See a solution process below:

First, we can factor the numerator and denominator as follows:

#((x - 3)(x + 1))/((x - 3)(x - 4))#

We can now cancel common terms in the numerator and denominator:

#(color(red)(cancel(color(black)((x - 3))))(x + 1))/(color(red)(cancel(color(black)((x - 3))))(x - 4)) => (x + 1)/(x - 4)#

However, from the original expression we need to ensure we don't divide by #0#.

#(x + 1)/(x - 4)# Where #x - 4 != 0# and #x - 3 !=0#

#(x + 1)/(x - 4)# Where #x != 4# and #x != 3#

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Answer 2

Isaiah Anthony

To simplify the expression (x^2-2x-3)/(x^2-7x+12), you can factor both the numerator and the denominator.

The numerator can be factored as (x-3)(x+1), and the denominator can be factored as (x-3)(x-4).

Now, you can cancel out the common factor of (x-3) from both the numerator and the denominator.

Therefore, the simplified expression is (x+1)/(x-4).

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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.