# What is the derivative of #y=(x^2 - 1) /( x+1)#?

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To find the derivative of ( y = \frac{x^2 - 1}{x + 1} ), you can use the quotient rule, which states that the derivative of a quotient of two functions is equal to the derivative of the numerator times the denominator minus the numerator times the derivative of the denominator, all divided by the square of the denominator.

Using the quotient rule, the derivative of ( y ) with respect to ( x ) is:

[ y' = \frac{(x + 1)(2x) - (x^2 - 1)(1)}{(x + 1)^2} ]

Simplify the expression:

[ y' = \frac{2x^2 + 2x - x^2 + 1}{(x + 1)^2} ] [ y' = \frac{x^2 + 2x + 1}{(x + 1)^2} ]

Therefore, the derivative of ( y = \frac{x^2 - 1}{x + 1} ) with respect to ( x ) is ( y' = \frac{x^2 + 2x + 1}{(x + 1)^2} ).

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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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