subtract the fractions

Question

4/x^2  -  16 - 3/x+4

Answer 1

First, I assume by the way the problem is typed that there are three terms, the last of which is 3/(x+4).

 

None of these 3 terms has a common factor, so the least common denominator is x²(x+4) = x³ + 4x².

 

You end up with [4(x+4) - 16(x³ + 4x²) - 3x^2]/(x³ + 4x²)

 

Grinding away at the numerator gives you -16x³ - 67x² + 4x + 16.

 

Your final answer is therefore (16 + 4x - 67x² - 16x³)/x³ + 4x²). (I like to begin polynomials with a positive term, hence the rearrangement.)

 

What a mess!