SOLUTION: Express as partial fractions: {{{((x^2-2x+4)/((2x)(x+1)(x-3)))}}} and {{{((-4y)/(3y^2-4y+1))}}} I know the answers are {{{(2/(3x)) + (7/(8(x+1))) + (7/(24(x-3)))}}} and {{

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Express as partial fractions: {{{((x^2-2x+4)/((2x)(x+1)(x-3)))}}} and {{{((-4y)/(3y^2-4y+1))}}} I know the answers are {{{(2/(3x)) + (7/(8(x+1))) + (7/(24(x-3)))}}} and {{      Log On


   

Question 866191: Express as partial fractions:
%28%28x%5E2-2x%2B4%29%2F%28%282x%29%28x%2B1%29%28x-3%29%29%29 and %28%28-4y%29%2F%283y%5E2-4y%2B1%29%29

I know the answers are %282%2F%283x%29%29+%2B+%287%2F%288%28x%2B1%29%29%29+%2B+%287%2F%2824%28x-3%29%29%29 and %282%2F%283x-1%29%29+-+%282%2F%28x-1%29%29
but I'm getting mixed up somewhere and not getting those answers... :/
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-2x%2B4=A%28x%2B1%29%28x-3%29%2B2Bx%28x-3%29%2B2Cx%28x%2B1%29
x%5E2-2x%2B4=A%28x%5E2-2x-3%29%2B%282Bx%5E2-6Bx%29%2B%282Cx%5E2%2B2Cx%29
x%5E2-2x%2B4=%28Ax%5E2-2Ax-3A%29%2B%282Bx%5E2-6Bx%29%2B%282Cx%5E2%2B2Cx%29
x%5E2-2x%2B4=%28A%2B2B%2B2C%29x%5E2%2B%28-2A-6B%2B2C%29x%2B%28-3A%29
Comparing terms,
1.A%2B2B%2B2C=1
.
.
2.-2A-6B%2B2C=-2
.
.
3.-3A=4
From eq. 3,
A=-4%2F3
Add eq. 1 and 2 together,
A%2B2B%2B2C%2B2A%2B6B-2C=1%2B2
3A%2B8B=3
-4%2B8B=3
8B=7
B=7%2F8
and finally,
A%2B2B%2B2C=1
-4%2F3%2B14%2F8%2B2C=1
2C=24%2F24%2B32%2F24-42%2F24
2C=14%2F24
C=7%2F24
.
.



.
.
.
%28%28-4y%29%2F%283y%5E2-4y%2B1%29%29=A%2F%283y-1%29+%2BB%2F%28y-1%29
-4y=A%28y-1%29%2BB%283y-1%29
-4y=Ay-A%2B3By-B
-4y=%28A%2B3B%29y%2B%28-A-B%29
Which leads to,
1.A%2B3B=-4
2.-A-B=0
From eq. 2,
A=-B
Substitute into eq. 1,
-B%2B3B=-4
2B=-4
B=-2
and
A=2
%28%28-4y%29%2F%283y%5E2-4y%2B1%29%29=A%2F%283y-1%29+%2BB%2F%28y-1%29
%28%28-4y%29%2F%283y%5E2-4y%2B1%29%29=2%2F%283y-1%29-2%2F%28y-1%29