please double check my work: partial fraction decomposition
3x/x^2-6x+9
factor the denominator
3x/(x-3)^2
so we have A/x-3+B/(x-3)^2
clear the denominator and left with
3x=A(x-3)+B
3x=Ax-3A+B
so A=3
and B=9

partial fraction decomposition would be
3/x-3+9/(x-3)^2
right?

Question

please double check my work: partial fraction decomposition
3x/x^2-6x+9
factor the denominator
3x/(x-3)^2
so we have A/x-3+B/(x-3)^2
clear the denominator and left with
3x=A(x-3)+B
3x=Ax-3A+B
so A=3
and B=9

partial fraction decomposition would be
3/x-3+9/(x-3)^2
right?

jhonyy9 · Answer

you will get 

     3x
-------
(x-3)*2

- so and with what and how you have continued sorry but i not can understanding

if you wan this can you write again like one multiply

   (3/x-3)(x/(x-3)= 3x/(x-3)*2

anonymous · Answer

You got it right. The work is perfect. If you want there is a short cut to partial fractions, but it doesn't always work. You can plug in values for x once you got your 3x=A(x-3)+B and make systems of equations or choose the x value to make things simplify nicely. For this problem pick x=3 because you will have 3*3=A(3-3)+B and then solve for B and then you can plug it in and find A. This isn't always the best way to do these problems, but sometimes it makes life easier. 

As you did this problem is the best way to go about partial fractions.