my last decomp of fractions: (11x^2 -32x+23)/(x-1)^2 (x-2)

[cjswonderfulgirl]

i have a problem originating in
(11x^2 -32x+23)/(x-1)^2 (x-2)
is the first step going to put it into A/x-2+B/x-1+C/(x-1)^2

 

[soroban]

Re: my last decomp of fractions, i promise!

Hello, cjswonderfulgirl!

You're off to a good start . . .

Partial fractions: .\(\displaystyle \frac{11x^2 -32x+23}{(x-1)^2 (x-2)}\)

Is the first step going to put it into: .\(\displaystyle \frac{A}{x-2} + \frac{B}{x-1} + \frac{C}{(x-1)^2}\)

I think you mean: .\(\displaystyle \frac{11x^2-32x + 23}{(x-1)^2(x-2)} \;=\;\frac{A}{x-2} + \frac{B}{x-1} + \frac{C}{(x-1)^2}\)


Then: .\(\displaystyle 11x^2 - 32x + 23 \;=\;A(x-1)(x-2) + B(x-2) + C(x-1)^2\)

. . and you're on your way!

 

[cjswonderfulgirl]

Re: my last decomp of fractions, i promise!

i got for my final answer 8/x-2 -2/x-1 +3/(x-1)^2 but my computer says it's wrong...so was i supposed to set it up as A/x-2 +B/x-1 +C/(x-1)^2?

 

[cjswonderfulgirl]

Re: my last decomp of fractions, i promise!

okay, my computer tells me i am supposed to use A/x-1 +B/(x-1)^2 +C/x-2
so i got 11x^2 -32x +23= A(x-1)^2 +B(x-2)(x-1) +C(x-2)
which is
A(x^2 -2x+1) +B(x^2 -3x+2) +C(x-2)
=(A+B)x^2 +(-2A-3B+C)x + (A+2B-2C)
which gives me
11=A+B
-32=-2A-3B+C
23=A+2B-2C
Solving to eliminate C i got
-32=-2A-3B+C(-2)
which is
-64=-4A-6B+2C
23 = A +2B-2C
which equals
-41=-3A-4B
then, solving to eliminate A i got
11=A+B(3)
which is
33=3A+3B
-41=-3A-4B
which gives me
-8=-1B so B=8
then plug that in to my first equation
11=A+8
so A=3
then i plug both of those into the last equation
23=3+2(8)-2C
20=16-2C
4=-2C
so C=-2
so altogether i got
(11x^2 -32x +23)/(x-1)^2 (x-2)=3/x-1 +8/(x-1)^2 -2/x-2
and i really don't know what i did wrong this time...:_(

 

[cjswonderfulgirl]

Re: my last decomp of fractions, i promise!

did i not do anything wrong? i would really really really REALLY appreciate help, and then i promise to leave you guys alone for a while i promise

 

[Deleted member 4993]

Re: my last decomp of fractions, i promise!

okay, my computer tells me i am supposed to use A/x-1 +B/(x-1)^2 +C/x-2
so i got 11x^2 -32x +23= A(x-1)^2 +B(x-2)(x-1) +C(x-2) <--- how's that? should be

A(x-1)(x-2) + B(x-2) + C(x-1)^2

because

the original denominator is (x-2)(x-1)^2