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

In adding and subtracting fractions, we need to have a common denominator.

The denominators are almost the same, but the signs in the second fraction are the wrong way around. We therefore need to do a 'switch-round'.

Now we have the same denominator and can add the fractions.

An alternative method would be to factorise first:

We still need to do a switch round in the second fraction. (The signs change in only ONE bracket)

Converting to a common denominator .

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To simplify the expression (3+y)/(y^2-9) - (y-3)/(9-y^2), we can start by factoring the denominators. The denominator y^2-9 can be factored as (y+3)(y-3), and the denominator 9-y^2 can be factored as (3+y)(3-y).

Next, we can find the least common denominator (LCD) of the two fractions, which is (y+3)(y-3)(3+y)(3-y).

Now, we can rewrite the expression using the LCD as follows: [(3+y)(3-y) - (y-3)(y+3)] / [(y+3)(y-3)(3+y)(3-y)].

Expanding the numerator, we get (9-y^2 - (y^2-9)) / [(y+3)(y-3)(3+y)(3-y)].

Simplifying further, we have (9-y^2 - y^2 + 9) / [(y+3)(y-3)(3+y)(3-y)].

Combining like terms in the numerator, we get 18 / [(y+3)(y-3)(3+y)(3-y)].

Therefore, the simplified expression is 18 / [(y+3)(y-3)(3+y)(3-y)].

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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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