How do you divide #(x^43x^32x^2+7x+3)/(x^2+3) #?
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To divide (x^43x^32x^2+7x+3) by (x^2+3), you can use long division. Here are the steps:

Divide the first term of the numerator (x^4) by the first term of the denominator (x^2). The result is x^2.

Multiply the entire denominator (x^2+3) by x^2, and subtract the result from the numerator. This gives you a new numerator: (x^43x^32x^2+7x+3)  (x^2)(x^2+3).

Simplify the new numerator: x^43x^32x^2+7x+3 + (x^4+3x^2).

Combine like terms in the numerator: 3x^3+7x+3.

Repeat the process by dividing the first term of the simplified numerator (3x^3) by the first term of the denominator (x^2). The result is 3x.

Multiply the entire denominator (x^2+3) by 3x, and subtract the result from the simplified numerator. This gives you a new numerator: 3x^3+7x+3  (3x)(x^2+3).

Simplify the new numerator: 3x^3+7x+3 + (3x^3+9x).

Combine like terms in the numerator: 16x+3.

Repeat the process by dividing the first term of the simplified numerator (16x) by the first term of the denominator (x^2). The result is 16.

Multiply the entire denominator (x^2+3) by 16, and subtract the result from the simplified numerator. This gives you a new numerator: 16x+3  16(x^2+3).

Simplify the new numerator: 16x+3  16x^248.

Combine like terms in the numerator: 16x^2+16x45.
The final result of the division is: x^2  3x  3 + (3x + 7)/(x^2+3) + 16/(x^2+3)  45/(x^2+3).
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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