# How do you simplify #(x^2 – 3x – 10)/(x^2 – 9)div(x^2 + 4x + 4)/(x+3)##?

First, factor your quadratic functions. Finding its roots will lead us to the factors and then it'll be way easier to calculate your result. So, let's find the roots (using Bhaskara)!

Rewriting:

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This explanation's going to be all math. I'm assuming you know how to factor polynomials, but if you don't, then don't be afraid to comment to ask how; I don't bite! Okay, let's start.

We can flip the 2nd fraction and multiply it.

Now let's factor the trinomials into binomials. Hopefully this will let us cancel out some stuff.

Now, I can cancel out some of the factors to simplify the answer.

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To simplify the expression, we can start by factoring the numerator and denominator separately.

The numerator (x^2 – 3x – 10) can be factored as (x – 5)(x + 2). The denominator (x^2 – 9) can be factored as (x – 3)(x + 3). The second fraction in the expression, (x^2 + 4x + 4)/(x + 3), can be simplified to (x + 2).

Now, we can rewrite the expression as [(x – 5)(x + 2)]/[(x – 3)(x + 3)] * (x + 2)/(x + 3).

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

This simplifies the expression to (x – 5)/(x – 3).

Therefore, the simplified form of the expression is (x – 5)/(x – 3).

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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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