document.write( "Question 65100: how do you do partial fraction decomposition?? Like on a problem such as: 1/(x^2+x)??? \n" ); document.write( "
Algebra.Com's Answer #45640 by venugopalramana(3286)\"\" \"About 
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1/(X^2+X)
\n" ); document.write( "1.FACTORISE D.R
\n" ); document.write( "X^2+X=X(X+1)
\n" ); document.write( "2.WRITE THE GIVEN EXPRESSION AS A SUM OF TERMS WITH EACH OF THE FACTORS IN D.R.
\n" ); document.write( "IF D.R IS DEGREE 1 PUT CONSTANTS LIKE A OR B OR C ETC IN THE N.R
\n" ); document.write( "IF D.R IS SECOND DEGREE PUT FIRST DEGREE BINOMIAL IN NR LIKE AX+B ETC
\n" ); document.write( "IF DR IS THIRD DEGREE PUT SECOND DEGREE TRINOMIAL IN NR..LIKE AX^2+BX+C ETC..
\n" ); document.write( "3. HERE D.R IS I DEGREE HENCE
\n" ); document.write( "1/(X^2+X) = [A/X] + [B/(X+1)]
\n" ); document.write( "SIMPLIFY RHS ...WE GET
\n" ); document.write( "1/X(X+1) = [A(X+1)+BX]/X(X+1)
\n" ); document.write( "EQUATE NRS AS DRS ARE SAME
\n" ); document.write( "1= A(X+1)+BX
\n" ); document.write( "GIVE DIFFERENT VALUES TO X ON LHS AND RHS TO GET EQNS TO SOLVE FOR A & B
\n" ); document.write( "GIVE X=0
\n" ); document.write( "1=A(0+1)=A...SO.A=1
\n" ); document.write( "GIVE X=-1
\n" ); document.write( "1=-B
\n" ); document.write( "B=-1
\n" ); document.write( "SO
\n" ); document.write( "[1/X(X+1)] = [1/X]- [1/(X+1)] \n" ); document.write( "
\n" );