# How do you simplify #(4y^3+12y^2-y-3)/(2y^3+y^2-18y-9)#?

We can factor our way through this:

The first two terms in the numerator and denominator seem to be comparable to the final two terms when viewed together:

We can now cancel on the following terms:

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To simplify the expression (4y^3+12y^2-y-3)/(2y^3+y^2-18y-9), you can factor both the numerator and denominator and then cancel out any common factors. Factoring the numerator and denominator, we get (y+3)(2y-1)(2y+1)/(y+3)(y-1)(2y+9). Canceling out the common factors (y+3) and (2y-1), the simplified expression is (2y+1)/(y-1)(2y+9).

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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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