How do you simplify #(x^2-3x-10)/(x^2-8x+15) * (x^2+5x-6)/(x^2+4x+4)#?

Answer 1

Let's start by factoring all of the expressions:

#(x^2-3x-10)/(x^2-8x+15) * (x^2+5x-6)/(x^2+4x+4)#
#((x-5)(x+2))/((x-5)(x-3)) * ((x+6)(x-1))/((x+2)(x+2)#
We can cancel out #(x-5) and (x+2)#.
#((x+6)(x-1))/((x-3)(x+2)#

FOILing in back in gives us:

#(x^2 + 6x - x -6)/(x^2 -3x + 2x -6)#
#(x^2 + 5x -6)/(x^2 -x- 6)#
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Answer 2

To simplify the expression (x^2-3x-10)/(x^2-8x+15) * (x^2+5x-6)/(x^2+4x+4), we can factorize the numerator and denominator of each fraction separately.

The first fraction can be factored as (x-5)(x+2)/(x-5)(x-3). The second fraction can be factored as (x-1)(x+6)/(x+2)(x+2).

Now, we can cancel out the common factors in the numerator and denominator.

(x-5) cancels out in the first fraction, and (x+2) cancels out in both fractions.

After canceling out the common factors, the expression simplifies to:

(x+6)/(x-3)

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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.

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.

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.

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.

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