The quotient and remainder, written as partial fractions will be [tex]4x-1 - \frac{2}{x +1} - \frac{3}{(x +2)^2}[/tex].
What are the Quotients?
Quotients are the number that is obtained by dividing one number by another number.
The degree of the numerator is the same as the degree of the denominator, this fraction needs to be simplified.
The rational expression is
[tex]\frac{4x^{3} +11x^{2} -9}{x^{2} +3x+2}[/tex]
Now, the denominator needs to be factored in to split up the second part of the simplified expression into two different partial fractions.
x^2 + 3 x + 2
( x + 1) (x + 2)
The general form of partial fractions.
[tex]A + \frac{B}{x +a} + \frac{C}{(x +a)^2}[/tex]
This gives us,
[tex]4x-1 - \frac{2}{x +1} - \frac{3}{(x +2)^2}[/tex]
Learn more about quotient ;
https://brainly.com/question/730603
