decomp of fractions for 3x^2 -11x-38/(x^2 -4)(x+1)

[cjswonderfulgirl]

hey, i have a question. i was decomposing this fraction and i hit a dead end because when i was trying to solve a system of equations, both my factors canceled out...here's what i got

original problem:3x^2 -11x-38/(x^2 -4)(x+1)

so then i got

3x^2 -11x-38/(x^2 -4)(x+1)=A/x-2 +B/x+2 +C/x+1

from which i got

3x^2 -11x-38=A(x+2)(x+1)+B(x-2)(x+1)+C(X-2)(x+2)

then

3x^2 -11x-38=(A+B+C)x^2 +(3A+B)x+(2A-2B-4C)

then my system of equations

3=A+B+C
-11=3A+B
-38=2A-2B-4C then i was solving:
3=A+B+C(4) =12=4A+4B+4C
-38=2A-2B-4C

which is -26=6A+2B

so, then i tried to cancel A or B using the second equation

-26=6A+2B
(-11=3A+B)(-2)

which is

-26=6A+2B
22=-6A-2B

so they both cancel out and now i'm VERY confused and i want to know where i went wrong....thanks

 

[stapel]

original problem:3x^2 -11x-38/(x^2 -4)(x+1)

What you have posted means the following:

. . . . .\(\displaystyle 3x^2\, -\, 11x\, -\, \frac{38}{(x^2\, -\, 4)(x\, +\, 1)}\)

I will guess that you mean the following:

. . . . .\(\displaystyle \frac{3x^2\, -\, 11x\, -\, 38}{(x^2\, -\, 4)(x\, +\, 1)}\)

If my guess is correct, then your initial set-up looks fine, assuming that you mean the denominators to include the three characters after the "slash", and that you're using "X" and "x" to really mean the same thing.

You might want to check your multiplication of "B" by (x - 2)(x + 1). You should not get B(x[sup:2670n3yk]2[/sup:2670n3yk] + 2x - 2).

:wink:

Eliz.

 

[royhaas]

Your second equation should be 3A-B = -11.

 

[galactus]

\(\displaystyle \frac{A}{x+2}+\frac{B}{x-2}+\frac{C}{x+1}=3x^{2}-11x-38\)

\(\displaystyle A(x-2)(x+1)+B(x+2)(x+1)+C(x+2)(x-2)=3x^{2}-11x-38\)

\(\displaystyle Ax^{2}+Bx^{2}+Cx^{2}-Ax+3Bx-2A+2B-4C=3x^{2}-11x-38\)

Equate coefficients:

\(\displaystyle A+B+C=3\)

\(\displaystyle -A+3B=-11\)

\(\displaystyle -2A+2B-4C=-38\Rightarrow {-A+B-2C=-19}\)

A=3B+11

3B+11+B+C=3--->4B+C+11=3---->C=-8-4B

-(3B+11)+B-2(-8-4B)=-19---->6B+5=-19--->B=-4

A=-1 and C=8

\(\displaystyle -\frac{1}{x+2}-\frac{4}{x-2}+\frac{8}{x+1}\)

Can you see what you're doing wrong?.

 

[cjswonderfulgirl]

i don't understand how you got -A+3B=-11. i checked, and it's right, i just thought that the 3 was with the A and not the B...