document.write( "Question 866191: Express as partial fractions:\r
\n" ); document.write( "\n" ); document.write( "\"%28%28x%5E2-2x%2B4%29%2F%28%282x%29%28x%2B1%29%28x-3%29%29%29\" and \"%28%28-4y%29%2F%283y%5E2-4y%2B1%29%29\"\r
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\n" ); document.write( "\n" ); document.write( "I know the answers are \"%282%2F%283x%29%29+%2B+%287%2F%288%28x%2B1%29%29%29+%2B+%287%2F%2824%28x-3%29%29%29\" and \"%282%2F%283x-1%29%29+-+%282%2F%28x-1%29%29\"\r
\n" ); document.write( "\n" ); document.write( "but I'm getting mixed up somewhere and not getting those answers... :/
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Algebra.Com's Answer #522193 by Fombitz(32388)\"\" \"About 
You can put this solution on YOUR website!

\n" ); document.write( "\"x%5E2-2x%2B4=A%28x%2B1%29%28x-3%29%2B2Bx%28x-3%29%2B2Cx%28x%2B1%29\"
\n" ); document.write( "\"x%5E2-2x%2B4=A%28x%5E2-2x-3%29%2B%282Bx%5E2-6Bx%29%2B%282Cx%5E2%2B2Cx%29\"
\n" ); document.write( "\"x%5E2-2x%2B4=%28Ax%5E2-2Ax-3A%29%2B%282Bx%5E2-6Bx%29%2B%282Cx%5E2%2B2Cx%29\"
\n" ); document.write( "\"x%5E2-2x%2B4=%28A%2B2B%2B2C%29x%5E2%2B%28-2A-6B%2B2C%29x%2B%28-3A%29\"
\n" ); document.write( "Comparing terms,
\n" ); document.write( "1.\"A%2B2B%2B2C=1\"
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\n" ); document.write( "2.\"-2A-6B%2B2C=-2\"
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\n" ); document.write( "3.\"-3A=4\"
\n" ); document.write( "From eq. 3,
\n" ); document.write( "\"A=-4%2F3\"
\n" ); document.write( "Add eq. 1 and 2 together,
\n" ); document.write( "\"A%2B2B%2B2C%2B2A%2B6B-2C=1%2B2\"
\n" ); document.write( "\"3A%2B8B=3\"
\n" ); document.write( "\"-4%2B8B=3\"
\n" ); document.write( "\"8B=7\"
\n" ); document.write( "\"B=7%2F8\"
\n" ); document.write( "and finally,
\n" ); document.write( "\"A%2B2B%2B2C=1\"
\n" ); document.write( "\"-4%2F3%2B14%2F8%2B2C=1\"
\n" ); document.write( "\"2C=24%2F24%2B32%2F24-42%2F24\"
\n" ); document.write( "\"2C=14%2F24\"
\n" ); document.write( "\"C=7%2F24\"
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\n" ); document.write( "\"%28%28-4y%29%2F%283y%5E2-4y%2B1%29%29=A%2F%283y-1%29+%2BB%2F%28y-1%29\"
\n" ); document.write( "\"-4y=A%28y-1%29%2BB%283y-1%29\"
\n" ); document.write( "\"-4y=Ay-A%2B3By-B\"
\n" ); document.write( "\"-4y=%28A%2B3B%29y%2B%28-A-B%29\"
\n" ); document.write( "Which leads to,
\n" ); document.write( "1.\"A%2B3B=-4\"
\n" ); document.write( "2.\"-A-B=0\"
\n" ); document.write( "From eq. 2,
\n" ); document.write( "\"A=-B\"
\n" ); document.write( "Substitute into eq. 1,
\n" ); document.write( "\"-B%2B3B=-4\"
\n" ); document.write( "\"2B=-4\"
\n" ); document.write( "\"B=-2\"
\n" ); document.write( "and
\n" ); document.write( "\"A=2\"
\n" ); document.write( "\"%28%28-4y%29%2F%283y%5E2-4y%2B1%29%29=A%2F%283y-1%29+%2BB%2F%28y-1%29\"
\n" ); document.write( "\"%28%28-4y%29%2F%283y%5E2-4y%2B1%29%29=2%2F%283y-1%29-2%2F%28y-1%29\"
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