Question 382940
{{{(2x+3)/(x^2+3x+2)=(2x+3)/((x+2)(x+1))}}}
{{{(2x+3)/(x^2+3x+2)=A/(x+2)+B/(x+1)}}}
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{{{2x+3=A(x+1)+B(x+2)}}}
{{{2x+3=Ax+Bx+A+2B}}}
{{{2x+3=(A+B)x+(A+2B)}}}
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1.{{{A+B=2}}}
2.{{{A+2B=3}}}
Subtract eq. 1 from eq. 2,
{{{A+2B-A-B=3-2}}}
{{{B=1}}}
Then from eq. 1,
{{{A+1=2}}}
{{{A=1}}}
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{{{highlight((2x+3)/(x^2+3x+2)=1/(x+2)+1/(x+1))}}}