Subtract the exponent

Question

Subtract 

4x^2/x−3 - x+1/x^2−9 What is the third term of the numerator of the difference when written in standard form?

Enter your answer as an expression, like this: 42x. If your expression contains exponents, use the ^ symbol. For example, if your answer is 42x^53, enter it like this: 42x^53.

Answer 1

First you need parenthesis around the denominator:

(4x^2)/(x-3) - (x-1)/(x^2-9) =

(4x^2)/(x-3) - (x-1)/[(x+3)(x-3)] = <--- factors

the missing factor is (x+3)/(x+3) in the first term:

(4x^2)(x+3) / (x^2-9) - (x+1)/(x^2-9) =

[(4x^2)(x+3) - (x+1)] / (x^2-9) =

[ 4x^3 + 12x^2 - x - 1]/(x^2 - 9)