document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=216791>Question 216791</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am trying to help my child but algebra was many years ago :-) .  I have the answer but I do not know how to get there.  Any help would be appreciated.\r<BR>\n" );
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document.write( "Split into a sum of two rational expressions with unlike denominators:\r<BR>\n" );
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document.write( "2x+3/(x^2+3x+2) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #163649 by </B><A HREF=/tutors/aboutme.mpl?userid=drj><B>drj(1380)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drj><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=drj><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=163649\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Split into a sum of two rational expressions with unlike denominators:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2B3%29%2F%28x%5E2%2B3x%2B2%29 ALIGN=MIDDLE  ALT=\"%282x%2B3%29%2F%28x%5E2%2B3x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 1.  This problem is called partial fraction expansion.\r<BR>\n" );
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document.write( "Factor the denominator where we need two integers m and n so that the sum is two and their product is 2.  That is m+n=3 and m*n=2.  \r<BR>\n" );
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document.write( "Step 2.  The two integers are 1 and 2.  So the denominator is factored as \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B3x%2B2=%28x%2B1%29%28x%2B2%29 ALIGN=MIDDLE  ALT=\"x%5E2%2B3x%2B2=%28x%2B1%29%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 3.   Substitute the factored denominator into the given equation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2B3%29%2F%28x%5E2%2B3x%2B2%29=%282x%2B3%29%2F%28x%2B1%29%28x%2B2%29 ALIGN=MIDDLE  ALT=\"%282x%2B3%29%2F%28x%5E2%2B3x%2B2%29=%282x%2B3%29%2F%28x%2B1%29%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 4.  Now what we want is the following \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2B3%29%2F%28x%2B1%29%28x%2B2%29=A%2F%28x%2B1%29%2BB%2F%28x%2B2%29 ALIGN=MIDDLE  ALT=\"%282x%2B3%29%2F%28x%2B1%29%28x%2B2%29=A%2F%28x%2B1%29%2BB%2F%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  where A and B are constants.\r<BR>\n" );
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document.write( "Once we find A and B we completed the problem.\r<BR>\n" );
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document.write( "Step 5.  So take the equation in Step 4 and multiply by (x+1)(x+2) to both sides of the equations in order to get rid of the denominators and to find A and B.  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29%28x%2B2%29%282x%2B3%29%2F%28x%2B1%29%28x%2B2%29=%28x%2B1%29%28x%2B2%29%2AA%2F%28x%2B1%29%2B%28x%2B1%29%28x%2B2%29%2AB%2F%28x%2B2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 6.  This will simplify by canceling common factors in both the numerator and denominator \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B3=A%2A%28x%2B2%29%2BB%2A%28x%2B1%29=Ax%2B2A%2BBx%2BB ALIGN=MIDDLE  ALT=\"2x%2B3=A%2A%28x%2B2%29%2BB%2A%28x%2B1%29=Ax%2B2A%2BBx%2BB\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B3=%28A%2BB%29x%2B2A%2BB ALIGN=MIDDLE  ALT=\"2x%2B3=%28A%2BB%29x%2B2A%2BB\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 7.  Now compare the left side and right side of the equation in Step 6:  Look at the x terms they must be equal and the numbers must be equal as well.  That is,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=%28A%2BB%29x ALIGN=MIDDLE  ALT=\"2x=%28A%2BB%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2=A%2BB ALIGN=MIDDLE  ALT=\"2=A%2BB\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Equation A1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3=2A%2BB ALIGN=MIDDLE  ALT=\"3=2A%2BB\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Equation B1\r<BR>\n" );
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document.write( "We have two Equations A1 and B1 and two unknown variables A and B:  \r<BR>\n" );
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document.write( "I can see that A=1 and B=1 will satisfy Equations A1 and B1\r<BR>\n" );
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document.write( "But, let's so through the process in finding A and B.\r<BR>\n" );
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document.write( "Let's subtract Equation B1 from Equation A1 to get:\r<BR>\n" );
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document.write( "2-3=A-2A+B-B or -1=-A or A=1  Then using Equation A1 to solve for B=2-1=1.\r<BR>\n" );
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document.write( "So A=1 and B=1.\r<BR>\n" );
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document.write( "Step 8.  ANSWER:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2B3%29%2F%28x%5E2%2B3x%2B2%29=%282x%2B3%29%2F%28x%2B1%29%28x%2B2%29=1%2F%28x%2B1%29%2B1%2F%28x%2B2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >  \r<BR>\n" );
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document.write( "I hope the above steps were helpful. \r<BR>\n" );
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document.write( "For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.\r<BR>\n" );
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document.write( "And good luck in your studies!\r<BR>\n" );
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document.write( "Respectfully,<BR>\n" );
document.write( "Dr J\r<BR>\n" );
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