Question 327895
{{{(x-6)/((x-2)(x-3))=A/(x-2)+B/(x-3)}}}
Multiply both sides by {{{(x-2)(x-3)}}}
{{{x-6=A(x-3)+B(x-2)}}}
{{{x-6=Ax+Bx-3A-2B}}}
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1.{{{A+B=1}}}
2.{{{3A+2B=6}}}
Multiply eq.1 by -3 and add the equations together to eliminate A.
{{{-3A-3B+3A+2B=-3+6}}}
{{{-B=3}}}
{{{highlight(B=-3)}}}
Then use either equation to solve for A.
{{{A-3=1}}}
{{{highlight(A=4)}}}
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{{{(x-6)/((x-2)(x-3))=4/(x-2)-3/(x-3)}}}