# How do you simplify and find the restrictions for #(3x-2)/(x+3)+7/(x^2-x-12)#?

Restrictions are

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To simplify the expression (3x-2)/(x+3)+7/(x^2-x-12), we first need to find the common denominator. The common denominator is (x+3)(x-4).

Next, we can rewrite the expression with the common denominator: [(3x-2)(x-4) + 7(x+3)] / [(x+3)(x-4)].

Expanding and combining like terms in the numerator gives: (3x^2 - 14x + 8 + 7x + 21) / [(x+3)(x-4)].

Simplifying further, we have: (3x^2 - 7x + 29) / [(x+3)(x-4)].

To find the restrictions, we need to identify any values of x that would make the denominator equal to zero. In this case, the restrictions are x = -3 and x = 4, as they would result in division by zero.

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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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