Write the form of the partial fraction decomposition of the rational expression. Do not solve for the constants. (Use A, B, and C for your constants.) (x^2 − 3x + 2)/(3x^3 + 11x^2)

my answer was (Ax+B)/x^2 + (A/3x+11) but it's wrong

Question

Write the form of the partial fraction decomposition of the rational expression. Do not solve for the constants. (Use A, B, and C for your constants.) (x^2 − 3x + 2)/(3x^3 + 11x^2) 

my answer was (Ax+B)/x^2 + (A/3x+11) but it's wrong

anonymous · Answer

(Ax+B)/x^2 + (C/3x+11) but it's wrong

earthcitizen · Answer

nasty, nasty lol
First, simplify the expression to 
$$(x-2)(x-1)$$
------------       
$$x ^{2}(3x+11)$$

earthcitizen · Answer

then transform,
$$(A/x ^{2}) + (B/x)+(C/(3x+11)$$

anonymous · Answer

that's it ? lol

anonymous · Answer

i thought if x^2 was the denominator, then the numerator would be liner, hence me putting Ax+B

earthcitizen · Answer

yh, i guess it's a different case

earthcitizen · Answer

multiply out by $$x ^{2}(3x+11)$$

anonymous · Answer

i'll try it later. i have to leave my house. thanks

earthcitizen · Answer

no p!

anonymous · Answer

A commented Mathematica solution is attached.

anonymous · Answer

Use the following attachment.  A comment error was corrected.