Partial fraction

**decoy808** · August 17th 2011, 07:53 AM

find the values of A,B and C such that

i see that it is repeated linear, but the x^2+4 is confusing me.

**FernandoRevilla** · August 17th 2011, 08:21 AM

Write

$\frac{2x-3}{(x+1)(x^2+4)}=\frac{A(x^2+4)+(Bx+C)(x+1)}{(x+1) (x^2+4)}$

and identify numerators.

**TheChaz** · August 17th 2011, 08:23 AM

"repeated linear" -?? I've never heard of that. Multiply by the LCD to get
$2x - 3 = A(x^2 + 4) + (Bx + C)(x + 1)$

$2x - 3 = Ax^2 + 4A + Bx^2 + (B + C)x + C$

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

Now equate coefficients.

**SammyS** · August 17th 2011, 05:29 PM

Originally Posted by TheChaz

"repeated linear" -?? I've never heard of that. Multiply by the LCD to get
$2x - 3 = A(x^2 + 4) + (Bx + C)(x + 1)$
...

Equate the numerators in FernandoRevilla's equation, and the result is exactly what you have in the above quote from your post.

**TheChaz** · August 17th 2011, 07:46 PM

True, though I'm not sure I get your point.

Expressing the terms with a common denominator and determining what's left after multiplying by the LCD are procedurally almost identical...

**SammyS** · August 17th 2011, 08:00 PM

Originally Posted by TheChaz

True, though I'm not sure I get your point.

Expressing the terms with a common denominator and determining what's left after multiplying by the LCD are procedurally almost identical...

Sorry about that Chaz. I didn't look at OP closely enough & thought that somehow you were referring to FernandoRevilla's Post.

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