graph of partial fraction

Jan 2010
142
0
I have a n equation of \(\displaystyle \frac{5x-3}{x(x^2-9)} \)

that needs to be write in partial fraction.

This i what I did:

\(\displaystyle \frac{5x-3}{x(x-3)(x+3)} \) = \(\displaystyle \frac{A}{x}+\frac{B}{x-3}+\frac{C}{x+3} \)

A= 1/3
B= 2/3
C= -1

result:
\(\displaystyle \frac{1}{3x}+\frac{2}{3(x-3)}-\frac{1}{x+3} \)

now here is the problem:

I have to graph the original and the result partial fraction and use the graphing calc with window [-6,6,1,-5,5,1,1] of both graph.

I don't know how to explain what i see in the graph...

Can you help me how to say it.. they are not the same when i graph it.
 

pickslides

MHF Helper
Sep 2008
5,237
1,625
Melbourne
Well let's start by recognising the values where there is no solution for \(\displaystyle x\). What are they? What is this called?