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How do you simplify #((x-3)/(x^2+3x+2))/((x^2-9)/(x+1))#?

Answer 1

Ethan Adkins

I tried this:

We can write it rearranging:

#(x-3)/((x+1)(x+2))*(x+1)/((x+3)(x-3))#

where we changed the fraction into a multiplication.

We may now simplify:

#cancel((x-3))/(cancel((x+1))(x+2))*cancel((x+1))/((x+3)cancel((x-3)))#

and be left with:

#1/((x+2)(x+3))#

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Answer 2

Jameson Allen

To simplify the expression ((x-3)/(x^2+3x+2))/((x^2-9)/(x+1)), we can follow these steps:

Factorize the denominators: x^2+3x+2 = (x+1)(x+2) x^2-9 = (x+3)(x-3)
Rewrite the expression using the factored denominators: ((x-3)/(x+1)(x+2))/((x+3)(x-3)/(x+1))
Invert the second fraction and multiply: ((x-3)/(x+1)(x+2)) * ((x+1)/(x+3)(x-3))
Cancel out common factors: (x-3)/(x+2) * 1/(x+3)
Simplify further if possible: (x-3)/(x+2(x+3))

Therefore, the simplified expression is (x-3)/(x+2(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.