# Thread: I'm having a problem with the following partial fraction

1. ## I'm having a problem with the following partial fraction

Why is it Ax(x+3) + B(x+3) + Cx^2
instead of Ax^2(x+3) + Bx(x+3) + Cx^3

2. Originally Posted by swatpup32

Why is it Ax(x+3) + B(x+3) + Cx^2
instead of Ax^2(x+3) + Bx(x+3) + Cx^3
hello
$\displaystyle \frac{A}{x}+\frac{B}{x^2}+\frac{C}{x+3}=\frac{Ax(x +3)+B(x+3)+Cx^2}{x^2(x+3)}$

3. I'm sorry, but I still don't understand.

4. Originally Posted by swatpup32
I'm sorry, but I still don't understand.
do you know how to make a single fraction of this expression, $\displaystyle \frac{A}{x}+\frac{B}{x^2}+\frac{C}{x+3}$ ?

5. okay, I wasn't thinking about it as a fraction. I was only considering the numerator. An, x canceled out from the numerator and denominator.

6. Originally Posted by Raoh
do you know how to make a single fraction of this expression, $\displaystyle \frac{A}{x}+\frac{B}{x^2}+\frac{C}{x+3}$ ?
you must make $\displaystyle \frac{A}{x}+\frac{B}{x^2}+\frac{C}{x+3}$ a single fraction with the denominator $\displaystyle x^2(x+3)$.

7. $\displaystyle \frac{x^2+8x-3}{x^2(x+3)}$$\displaystyle =\frac{Ax(x+3)+B(x+3)+Cx^2}{x^2(x+3)}$
now get rid of the same denominators and you'll have,
$\displaystyle x^2+8x-3=Ax(x+3)+B(x+3)+Cx^2$