Wednesday

August 27, 2014

August 27, 2014

Posted by **Jamie** on Monday, December 17, 2012 at 1:11am.

or

-1=A(x^2+3x+9)+Bx+C(x-3)

I'm trying to find the partial fraction decomposition. I think A=-1/21, but how do I find the right values to plug in for x to find B and C?

- Math -
**Steve**, Monday, December 17, 2012 at 4:15amDo a cross-multiply to put all over a common denominator:

(Ax+B)/(x^2+3x+9) + C/(x-3)

= [(Ax+B)(x-3) + C(x^2+3x+9)]/(x^3-27)

= (Ax^2+(B-3A)x-3B+Cx^2+3Cx+9C)/(x^3-27)

= [(A+C)x^2 + (B-3A+3C)x + (9C-3B)] / (x^3-27)

So, for the numerators to be identical, coefficients of like powers must be equal:

A+C = 0

B-3A+3C = 0

9C-3B = -1

(A,B,C) = (1/27, 6/27, -1/27)

so, -1/(x^3-27) = (x+6)/(27(x^2+3x+9)) - 1/(27(x-3))

**Related Questions**

Math - Find the partial fraction decomposition for the ration expression. (4x^2...

Algebra - Below is my problem with my answers. I don't think this is that tough...

chemistry - The time dependent concentration of solute particles in a solution ...

calculus - Write the form of the partial fraction decomposition of the function ...

partial fractions - (7x^2-16)/(x^2-2x) solve by using partial fraction ...

Chem - A gas mixture in a 3.100 L container at 415°C contains 1.30 g each of Ar...

calculus - Integral of 10 / (5x^2 - 2x^3) Do not determine the numerical values ...

math - trying to find a fraction riddle. I'm a fraction greater than 1/2 and ...

math - how do you integrate 30x^2/((x-2)(x+3)(x-5)) using partial fraction ...

Math - please help - If x and y are in the interval (0,π/12) and sin x = 3/...