Question

Please help!!! :)




partial fraction of 3/ x^2-3x

Answer 1

Start by factoring the denominator.
\[3/((x)(x-3))\]

This one is relatively simple to break up; to linear factors.

\[A/x+B(x-3)=3/(x^2-3x)\]

Now we clear the denominators....

\[A(x-3)+B(x)=3\]

Using this, we generate a system of equations by equating the coefficients

A+B=0x---(this equation corresponds to the X coefficients)
-3A+0B=3----(this equation corresponds to the constants)

If you're completely unsure of how to start the problem, your best bet is checking a textbook; I kind of blew through an explanation; hopefully it jogged your memory if you've seen it before.

Answer 2

Also, from the system of equations, we know that A=-1 and B=1

This means that our final answer(our partial fraction decomposition) is

\[-1/x+1/(x-3)\]

Answer 3

thank you so so so much!!! :)