# How do you simplify #(4z)/(z - 4) + (z + 4)/(z + 1)#?

Make equivalent fractions:

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To simplify the expression (4z)/(z - 4) + (z + 4)/(z + 1), we need to find a common denominator and combine the fractions. The common denominator is (z - 4)(z + 1).

Multiplying the first fraction by (z + 1)/(z + 1) and the second fraction by (z - 4)/(z - 4), we get:

[(4z)(z + 1) + (z + 4)(z - 4)] / [(z - 4)(z + 1)]

Expanding and simplifying the numerator, we have:

(4z^2 + 4z + z^2 - 16) / [(z - 4)(z + 1)]

Combining like terms in the numerator, we get:

(5z^2 + 4z - 16) / [(z - 4)(z + 1)]

Therefore, the simplified expression is (5z^2 + 4z - 16) / [(z - 4)(z + 1)].

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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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