document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1001737>Question 1001737</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1-y^2/y^2+4y+3<BR>\n" );
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document.write( "5x^2-125/2x^2-9x-5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #618826 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52809)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=618826\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "There is no question in your submitting.<BR>\n" );
document.write( "Also there is no necessary parentheses in it.<BR>\n" );
document.write( "It is incomplete.<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- If your submission is correct and completed;<BR>\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- if the problem is of the school Math curricculum or closely adjacent to it;<BR>\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- if the condition is reasonable and reasonably formulated then . . . \r<BR>\n" );
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document.write( "then the chances are high enough that you will get the solution from the tutors.\r<BR>\n" );
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document.write( "In opposite, if some of these circumstances are not in the place, <BR>\n" );
document.write( "then you hardly can expect to get the solution or even the response.\r<BR>\n" );
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document.write( "In case your submission was failed and your tutor pointed you in it, <BR>\n" );
document.write( "do not become furious. &nbsp;Be polite and say &nbsp;\"Thank you\" &nbsp;to your teacher . . . <BR>\n" );
document.write( "(. . . Besides of all, &nbsp;it is much more productive).\r<BR>\n" );
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document.write( "Then think what was your mistake and how to fix it. &nbsp;You can resubmit your request.\r<BR>\n" );
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document.write( "<U>Comment from student</U>: &nbsp;The question is to simplify those two problems.<BR>\n" );
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document.write( "OK, &nbsp;let's do it.\r<BR>\n" );
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document.write( "1. &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281-y%5E2%29%2F%28y%5E2%2B4y%2B3%29 ALIGN=MIDDLE  ALT=\"%281-y%5E2%29%2F%28y%5E2%2B4y%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;The polynomial in the numerator can be factored &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-y%5E2 ALIGN=MIDDLE  ALT=\"1-y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = (1+y)*(1-y).\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;The polynomial in the denominator can be factored &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2%2B4y%2B3 ALIGN=MIDDLE  ALT=\"y%5E2%2B4y%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = (y+1)*(y+3).\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;Thus &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281-y%5E2%29%2F%28y%5E2%2B4y%2B3%29 ALIGN=MIDDLE  ALT=\"%281-y%5E2%29%2F%28y%5E2%2B4y%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%281%2By%29%2A%281-y%29%29%2F%28%28y%2B1%29%2A%28y%2B3%29%29 ALIGN=MIDDLE  ALT=\"%28%281%2By%29%2A%281-y%29%29%2F%28%28y%2B1%29%2A%28y%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(reduce the numerator and the denominator by the factor (1+y) ) &nbsp;&nbsp;-----> \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28cross%28%281%2By%29%29%2A%281-y%29%29%2F%28cross%28%28y%2B1%29%29%2A%28y%2B3%29%29 ALIGN=MIDDLE  ALT=\"%28cross%28%281%2By%29%29%2A%281-y%29%29%2F%28cross%28%28y%2B1%29%29%2A%28y%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281-y%29%2F%28y%2B3%29 ALIGN=MIDDLE  ALT=\"%281-y%29%2F%28y%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "2. &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285x%5E2-125%29%2F%282x%5E2-9x-5%29 ALIGN=MIDDLE  ALT=\"%285x%5E2-125%29%2F%282x%5E2-9x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;The numerator can be factored &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2-125 ALIGN=MIDDLE  ALT=\"5x%5E2-125\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 5*(x+5)*(x-5). \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;The denominator can be factored &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2-9x-5 ALIGN=MIDDLE  ALT=\"2x%5E2-9x-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > = (x-5)*(2x+1). &nbsp;&nbsp;&nbsp;&nbsp;(You can get this factoring by finding the roots of the quadratic polynomial). \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;Thus &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285x%5E2-125%29%2F%282x%5E2-9x-5%29 ALIGN=MIDDLE  ALT=\"%285x%5E2-125%29%2F%282x%5E2-9x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2A%28x-5%29%2A%28x%2B5%29%29%2F%28%28x-5%29%2A%282x%2B1%29%29 ALIGN=MIDDLE  ALT=\"%285%2A%28x-5%29%2A%28x%2B5%29%29%2F%28%28x-5%29%2A%282x%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(reduce the numerator and the denominator by the factor (x-5) ) &nbsp;&nbsp;-----> \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2Across%28%28x-5%29%29%2A%28x%2B5%29%29%2F%28cross%28%28x-5%29%29%2A%282x%2B1%29%29 ALIGN=MIDDLE  ALT=\"%285%2Across%28%28x-5%29%29%2A%28x%2B5%29%29%2F%28cross%28%28x-5%29%29%2A%282x%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2A%28x%2B5%29%29%2F%282x%2B1%29 ALIGN=MIDDLE  ALT=\"%285%2A%28x%2B5%29%29%2F%282x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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