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Partial fractions from a single fraction?

I've just started to study this and I'm stuck as hell on a question in my text book. I cannot for the life of me see how they get the answer they do. Can someone please explain the procedure?

The algebraic fraction is:

3x+9 / x2 + 8x + 12

When I work this out I get partial fractions of:

0.75 / x+2 + -0.25 / x+6 (the numerators are fractions themselves)

The answer given in the book is:

1/4 (3/x+2 + 9/x+6)


Oh... and can someone point me towards a tutorial for writing mathematical formula, fractions etc. correctly please? I know there's one on here somewhere but I can't find it now.
(edited 6 years ago)
Original post by Darwinion
I've just started to study this and I'm stuck as hell on a question in my text book. I cannot for the life of me see how they get the answer they do. Can someone please explain the procedure?

The algebraic fraction is:

3x+9 / x2 + 8x + 12

When I work this out I get partial fractions of:

0.75 / x+2 + -0.25 / x+6 (the numerators are fractions themselves)

The answer given in the book is:

1/4 (3/x+2 + 9/x+6)


Oh... and can someone point me towards a tutorial for writing mathematical formula, fractions etc. correctly please? I know there's one on here somewhere but I can't find it now.


Well you've got the first fraction right anyway, so I assume you're making a mistake at some point when it comes to finding the numerator of the other fraction.

3x+9x2+8x+12=3x+9(x+2)(x+6)=Ax+2+Bx+6=Ax+6A+Bx+2B(x+2)(x+6)\displaystyle \frac{3x+9}{x^2+8x+12}=\frac{3x+9}{(x+2)(x+6)}= \frac{A}{x+2}+ \frac{B}{x+6}=\frac{Ax+6A+Bx+2B}{(x+2)(x+6)}

Means Ax+Bx=3xAx+Bx=3x and 6A+2B=96A+2B=9

And since you know that A=34A=\frac{3}{4} then you can find BB since you know that B=3−AB=3-A from eq 1


http://www.thestudentroom.co.uk/wiki/LaTex
(edited 6 years ago)
Reply 2
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Darwinion
OP
12
Thanks for that! I dunno what I was doing for calculating B. The way you laid it out quite clearly shows that B=214B=2\frac{1}{4}

Yay... and I got the LaTex right :tongue: That's gonna need some practice though.
(edited 6 years ago)

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