Question 395282
set up the following equation
{{{(9x^2-24x-57)/((x+1)(x+3)(x-5))=A/(x+1)+B/(x+3)+C/(x-5)}}}
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next multiply both sides by the common denominator (x+1)(x+3)(x-5)
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{{{(9x^2-24x-57)=A(x+3)(x-5)+B(x+1)(x-5)+C(x+1)(x+3)}}}
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at this point you can expand out all terms, then combined common terms and set correponding parts equal yielding a system of equation to solve for A,B and C
but another alternative is to select "convenient values of x and solve 
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x=-1:  {{{9(-1)^2-24(-1)-57=A(-1+3)(-1-5)+B*0+C*0}}}
9+24-57=-12A or A=-24/-12=2
x=-3:   {{{9(-3)^2-24(-3)-57=A*0+B*(-3+1)(-3-5)+C*0}}}
81+72-57=72B  or B=96/72=4/3
x=5:  {{{9(5)^2-24(5)-57=A*0+B*0+C*(5+1)(5+3)}}}
225-120-57=48C or C=48/48=1
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if I did my math correctly
{{{(9x^2-24x-57)/((x+1)(x+3)(x-5))=2/(x+1)+4/(3(x+3))+1/(x-5)}}}