Question 1184482
{{{A^""/(x^""+1) + B^""/(x^""+2) + C^""/(x^""-3) = (2x^2-6x+6) / ((x^""-1)(x^""-2)(x^""-3))}}}
<pre>
I'll bet this was a partial fraction problem and you copied the wrong
denominators either on the left side or the right side. However, I'll
solve the problem that you posted anyway:

Substituting x=0 and simplifying

{{{A^""/(0^""+1) + B^""/(0^""+2) + C^""/(0^""-3) = (2(0)^2-6(0)+6) / ((0^""-1)(0^""-2)(0^""-3))}}}

{{{A/(1) + B/(2) + C/(-3) = (0-0+6) / (-1)(-2)(-3))}}}

{{{A + B/2 - C/3 = 6/(-6)}}}

{{{A + B/2 - C/3 = -1}}}

{{{6A + 3B - 2C = -6}}}

Substituting x=4 and simplifying

{{{A^""/(4^""+1) + B^""/(4^""+2) + C^""/(4^""-3) = (2(4)^2-6(4)+6) / ((4^""-1)(4^""-2)(4^""-3))}}}

{{{A/5 + B/6 + C/1 = (32-24+6) / ((3)(2)(1))}}}

{{{A/5 + B/6 + C = 14/6}}}

{{{6A+5B+30C=70}}}

Substituting x=-3 and simplifying

{{{A^""/(-3^""+1) + B^""/(-3^""+2) + C^""/(-3^""-3) = (2(-3)^2-6(-3)+6) / ((-3^""-1)(-3^""-2)(-3^""-3))}}}

{{{A/(-2) + B/(-1) + C/(-6) = (2(9)+18+6) / ((-4)(-5)(-6))}}}

{{{-A/2 - B - C/6 = (18+18+6) / (-120)}}}

{{{-A/2 - B - C/6 = 42/(-120)}}}

{{{-A/2 - B - C/6 = -42/120}}}

{{{-A/2 - B - C/6 = -7/20}}}

{{{-30A - 60B-10C = -21}}}

{{{30A + 60B+10C = 21}}}

Solve the system:

{{{system(6A + 3B - 2C = -6,6A+5B+30C=70, 30A + 60B+10C = 21)}}}

Solve that system and get 

{{{A = -1/4}}}, {{{B = 2/25}}}, {{{C = 237/100}}}

Then your answer would be:

{{{(-1/4)/(x^""+1) + (2/25)/(x^""+2) + (237/100)/(x^""-3) = (2x^2-6x+6) / ((x^""-1)(x^""-2)(x^""-3))}}}

{{{-1/(4(x+1))+2/(25(x+2))+237/(100(x-3))= (2x^2-6x+6) / ((x^""-1)(x^""-2)(x^""-3))}}}

But I'll bet you you copied those denominators wrong!!!!

Edwin</pre>