document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=75282>Question 75282</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi I need help with rational equations. The Directions say to Factor First then solve the equation. \r<BR>\n" );
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document.write( "1. x/(x+3) + 1/(x-1)= 4/ x^2+2x-3 \r<BR>\n" );
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document.write( "2. 2/(x-1) - x/(x+3)= 6/ x^2+2x-3\r<BR>\n" );
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document.write( "3. 1/(y^2-16)- 2/(y+4)= 2/(y-4)\r<BR>\n" );
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document.write( "If you can help me with these and explain them I would very much appriciate <BR>\n" );
document.write( "it. The TextBook I'm using is Algebra 1 Concepts and Skills by McDougal. AND im on Chaper 11.7 \r<BR>\n" );
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document.write( "thank you.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #54037 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=54037\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Problem #1<BR>\n" );
document.write( "First of all, is the right side of the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2Fx%5E2%29%2B2x-3 ALIGN=MIDDLE  ALT=\"%284%2Fx%5E2%29%2B2x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > or is it<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F%28x%5E2%2B2x-3%29 ALIGN=MIDDLE  ALT=\"4%2F%28x%5E2%2B2x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >????  I will assume it's the latter and I will make the same assumption for problem #2.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F%28x%2B3%29%2B1%2F%28x-1%29=4%2F%28x%5E2%2B2x-3%29 ALIGN=MIDDLE  ALT=\"x%2F%28x%2B3%29%2B1%2F%28x-1%29=4%2F%28x%5E2%2B2x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Note that we can factor first <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2x-3 ALIGN=MIDDLE  ALT=\"x%5E2%2B2x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29%28x-1%29 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  so we have:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F%28x%2B3%29%2B1%2F%28x-1%29=4%2F%28x%2B3%29%28x-1%29 ALIGN=MIDDLE  ALT=\"x%2F%28x%2B3%29%2B1%2F%28x-1%29=4%2F%28x%2B3%29%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Now we will multiply each term by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29%28x-1%29 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which is the LCM and this will get rid of the fractions\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%28x%2B3%29%28x-1%29%29%2F%28x%2B3%29%2B%28%28x%2B3%29%28x-1%29%29%2F%28x-1%29=%284%28x%2B3%29%28x-1%29%29%2F%28x%2B3%29%28x-1%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > start canceling terms in the numerator and denominator and when we get through, we have:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x-1%29%2B%28x%2B3%29=4 ALIGN=MIDDLE  ALT=\"x%28x-1%29%2B%28x%2B3%29=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > get rid of parens\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-x%2Bx%2B3=4 ALIGN=MIDDLE  ALT=\"x%5E2-x%2Bx%2B3=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >  subtract 3 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-x%2Bx%2B3-3=4-3 ALIGN=MIDDLE  ALT=\"x%5E2-x%2Bx%2B3-3=4-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > collect like terms<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=1 ALIGN=MIDDLE  ALT=\"x%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > take square root of both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=plus+or+minus+1 ALIGN=MIDDLE  ALT=\"x=plus+or+minus+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Problem #2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F%28x-1%29+-+x%2F%28x%2B3%29=+6%2F%28x%5E2%2B2x-3%29 ALIGN=MIDDLE  ALT=\"2%2F%28x-1%29+-+x%2F%28x%2B3%29=+6%2F%28x%5E2%2B2x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  we will factor first<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F%28x-1%29-x%2F%28x%2B3%29=6%2F%28x%2B3%29%28x-1%29 ALIGN=MIDDLE  ALT=\"2%2F%28x-1%29-x%2F%28x%2B3%29=6%2F%28x%2B3%29%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now we will multiply each term by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29%28x-1%29 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which is the LCM and this will get rid of the fractions---same as before but this time I will cancel out terms as we go:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x%2B3%29-x%28x-1%29=6 ALIGN=MIDDLE  ALT=\"2%28x%2B3%29-x%28x-1%29=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > get rid of parens\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B6-x%5E2%2Bx=6 ALIGN=MIDDLE  ALT=\"2x%2B6-x%5E2%2Bx=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >  subtract 6 from both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B6-6-x%5E2%2Bx=6-6 ALIGN=MIDDLE  ALT=\"2x%2B6-6-x%5E2%2Bx=6-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > collect like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%5E2%2B3x=0 ALIGN=MIDDLE  ALT=\"-x%5E2%2B3x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >multiply both sides by -1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-3x=0 ALIGN=MIDDLE  ALT=\"x%5E2-3x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >  factor<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x-3%29=0 ALIGN=MIDDLE  ALT=\"x%28x-3%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3 ALIGN=MIDDLE  ALT=\"x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Problem #3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28y%5E2-16%29-+2%2F%28y%2B4%29=+2%2F%28y-4%29 ALIGN=MIDDLE  ALT=\"1%2F%28y%5E2-16%29-+2%2F%28y%2B4%29=+2%2F%28y-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We can factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%5E2-16%29=%28y%2B4%29%28y-4%29 ALIGN=MIDDLE  ALT=\"%28y%5E2-16%29=%28y%2B4%29%28y-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  so we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28y%2B4%29%28y-4%29-+2%2F%28y%2B4%29=+2%2F%28y-4%29 ALIGN=MIDDLE  ALT=\"1%2F%28y%2B4%29%28y-4%29-+2%2F%28y%2B4%29=+2%2F%28y-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Now we will multiply each term by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%2B4%29%28y-4%29 ALIGN=MIDDLE  ALT=\"%28y%2B4%29%28y-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which is the LCM and this will get rid of the fractions---same as before but this time I will cancel out terms as we go:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-2%28y-4%29=2%28y%2B4%29 ALIGN=MIDDLE  ALT=\"1-2%28y-4%29=2%28y%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > get rid of the parens\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-2y%2B8=2y%2B8 ALIGN=MIDDLE  ALT=\"1-2y%2B8=2y%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" >  subtract 2y and 8 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-2y-2y%2B8-8=2y-2y%2B8-8 ALIGN=MIDDLE  ALT=\"1-2y-2y%2B8-8=2y-2y%2B8-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > collect like terms<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-4y=0 ALIGN=MIDDLE  ALT=\"1-4y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >  subtract 1 from each side \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-1-4y=-1 ALIGN=MIDDLE  ALT=\"1-1-4y=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >  collect like terms<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4y=-1 ALIGN=MIDDLE  ALT=\"-4y=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > divide both sides by -4<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1%2F4 ALIGN=MIDDLE  ALT=\"y=1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "A good drill for you is to plug the answers in and see if they work\r<BR>\n" );
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document.write( "Hope this helps----ptaylor\r<BR>\n" );
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