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

first, factorise each expression.

putting the factorised expressions into the question gives

this can be cancelled

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To simplify the expression (x^2 + x - 6)/(x^2 - 4) * (x^2 - 9)/( x^2 + 6x + 9), we can factor the numerator and denominator of each fraction and then cancel out any common factors.

The numerator of the first fraction, x^2 + x - 6, can be factored as (x + 3)(x - 2). The denominator of the first fraction, x^2 - 4, can be factored as (x + 2)(x - 2).

The numerator of the second fraction, x^2 - 9, can be factored as (x + 3)(x - 3). The denominator of the second fraction, x^2 + 6x + 9, can be factored as (x + 3)(x + 3), which is equivalent to (x + 3)^2.

Now, we can cancel out the common factors in the numerator and denominator: (x + 3)(x - 2)/(x + 2)(x - 2) * (x + 3)(x - 3)/(x + 3)^2

After canceling out the common factors, we are left with: (x - 2)/(x + 2) * (x - 3)/(x + 3)

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