document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=597185>Question 597185</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If I have a problem like this one I am not sure how to even start to simplify it. The directions say Perfom the indicated operations and simplify: \r<BR>\n" );
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document.write( "    x+3y                   x+y                     x+2y<BR>\n" );
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document.write( "4(x^2)+12xy+8(y^2)     4(x^2)+20xy+24(y^2)     4(x^2)+16xy+12(y^2)\r<BR>\n" );
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document.write( "I tried to take ouf a 4 of each denominator then got stuck, can you help? the numerators are x+3y, x+y, and x+2y, they wont let me put them right, sorry </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #378246 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=378246\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You are right in thinking that you need to do some factoring and taking out a 4 from each denominator is a good start.<BR>\n" );
document.write( "I'll show you the next steps, and what clues and tricks I used.<BR>\n" );
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document.write( "THE SOLUTION (skipping explanations for now):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3y%29%2F%284x%5E2%2B12xy%2B8y%5E2%29-%28x%2By%29%2F%284x%5E2%2B20xy%2B24y%5E2%29%2B%28x%2B2y%29%2F%28+4x%5E2%2B16xy%2B12y%5E2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3y%29%2F%284%28x%5E2%2B3xy%2B2y%5E2%29%29-%28x%2By%29%2F%284%28x%5E2%2B5xy%2B6y%5E2%29%29%2B%28x%2B2y%29%2F%284%28x%5E2%2B4xy%2B3y%5E2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3y%29%2F%284%28x%2By%29%28x%2B2y%29%29-%28x%2By%29%2F%284%28x%2B2y%29%28x%2B3y%29%29%2B%28x%2B2y%29%2F%284%28x%2By%29%28x%2B3y%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2B3y%29%5E2-%28x%2By%29%5E2%2B%28x%2B2y%29%5E2%29%2F%284%28x%2By%29%28x%2B2y%29%28x%2B3y%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%5E2%2B6xy%2B9y%5E2%29+-%28x%5E2%2B2xy%2By%5E2%29%2B%28x%5E2%2B4xy%2B4y%5E2%29%29%2F%284%28x%2By%29%28x%2B2y%29%28x%2B3y%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2B6xy%2B9y%5E2-x%5E2-2xy-y%5E2%2Bx%5E2%2B4xy%2B4y%5E2%29%2F%284%28x%2By%29%28x%2B2y%29%28x%2B3y%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2B8xy%2B12y%5E2%29%2F%284%28x%2By%29%28x%2B2y%29%28x%2B3y%29%29 ALIGN=MIDDLE  ALT=\"%28x%5E2%2B8xy%2B12y%5E2%29%2F%284%28x%2By%29%28x%2B2y%29%28x%2B3y%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2B2y%29%28x%2B6y%29%29%2F%284%28x%2By%29%28x%2B2y%29%28x%2B3y%29%29 ALIGN=MIDDLE  ALT=\"%28%28x%2B2y%29%28x%2B6y%29%29%2F%284%28x%2By%29%28x%2B2y%29%28x%2B3y%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B6y%29%2F%284%28x%2By%29%28x%2B3y%29%29 ALIGN=MIDDLE  ALT=\"%28x%2B6y%29%2F%284%28x%2By%29%28x%2B3y%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "ABOUT FACTORING:<BR>\n" );
document.write( "When you have a polynomial with x and y, like<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B3xy%2B2y%5E2 ALIGN=MIDDLE  ALT=\"x%5E2%2B3xy%2B2y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "factoring may look complicated, but there are clues and tricks that helped me factor it.<BR>\n" );
document.write( "I noticed that he total degree (in x and y) of all the terms is 2, so I knew that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B3xy%2B2y%5E2=y%5E2%28x%5E2%2Fy%5E2%2B3x%2Fy%2B2%29=y%5E2%28%28x%2Fy%29%5E2%2B3%28x%2Fy%29%2B2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and renaming variables using <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=x%2Fy ALIGN=MIDDLE  ALT=\"z=x%2Fy\"   DISABLED_style= \"max-width:90%; height:auto;\" > the big bracket turns into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E2%2B3z%2B2 ALIGN=MIDDLE  ALT=\"z%5E2%2B3z%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I knew I could handle that.<BR>\n" );
document.write( "It is easier to factor when there is only one variable, and if it seemed difficult I could always resort to the quadratic formula to find that the zeros of that polynomial. It would tell me that the zeros are z=-1 and z=-2, and from there I would figure out that the factors are (z+1) and (z+2). </SPAN>\n" );
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