# How do you add or subtract #(y^2-5)/(y^4-81) + 4/(81-y^4)#?

We can rewrite this sum as

Using the l.c.d.:

That can be your final answer, but let's draw attention to the fact we have factorable functions there.

Now, as for the denominator:

Let's just go slowly here and take the square root of both sides.

Therefore, your "final" answer can be rewritten as

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To add or subtract the given expressions, we need to find a common denominator. In this case, the common denominator is (y^4 - 81).

To add the fractions, we multiply the numerator and denominator of the first fraction by (81 - y^4), and the numerator and denominator of the second fraction by (y^4 - 81).

This gives us:

[(y^2 - 5)(81 - y^4)] / [(y^4 - 81)(81 - y^4)] + [4(y^4 - 81)] / [(y^4 - 81)(81 - y^4)]

Simplifying the numerators, we have:

[(81y^2 - 405 - 81y^4 + 5y^2)] / [(y^4 - 81)(81 - y^4)] + [4y^4 - 324] / [(y^4 - 81)(81 - y^4)]

Combining like terms in the numerators, we get:

[(86y^2 - 81y^4 - 405)] / [(y^4 - 81)(81 - y^4)] + [4y^4 - 324] / [(y^4 - 81)(81 - y^4)]

Now, we can combine the fractions by adding the numerators:

[(86y^2 - 81y^4 - 405 + 4y^4 - 324)] / [(y^4 - 81)(81 - y^4)]

Simplifying the numerator further:

[(86y^2 - 77y^4 - 729)] / [(y^4 - 81)(81 - y^4)]

Therefore, the simplified expression is:

(86y^2 - 77y^4 - 729) / (y^4 - 81)(81 - y^4)

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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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