x² + 1
x³ + 2x

Dividing a Polynomial by a Polynomial is similar to that of dividing whole numbers.

The answer is going to be  \frac{1}{x} +  \frac{3}{ x^{3}+ 2x  }

Solution is on the image I uploaded, just take a look of it.

Step 1:
Divide x^2 by x^3, (first term of the dividend by the first term of the divisor) that will result to 1/x

Step 2:
Multiply 1/x by the terms of the divisor, that will result to x^2 and +2. 

Step 3:
Subtract x^2 +2 from x^2 +1, which results to -1.

Explanation 101:
Hence, (x^2 + 1) / (x^3 + 2x) = 1/x remainder of -1. The quotient can also be expressed as:

 \frac{1}{x} -  \frac{1}{x^3 + 2x}


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