document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=445209>Question 445209</A>: <I><SPAN STYLE=\"word-break: break-all;\"> i'm trying to show a=b or a=1/b without plugging in the values for a.\r<BR>\n" );
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document.write( "this is the equation\r<BR>\n" );
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document.write( "a+1/a=b+1/b\r<BR>\n" );
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document.write( "i have tried multiplying both sides by ab<BR>\n" );
document.write( "i tried the quadratic equation but that didn't work very well cause i couldn't get the square root out\r<BR>\n" );
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document.write( "i just need a step by step explanation of how to get there cause its driving me crazy and i think i'm just missing something simple\r<BR>\n" );
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document.write( "please remember. i know how to substitute. i'm basically proving a= b,1/b<BR>\n" );
document.write( "which is why i tried making it a quadratic because i knew there were 2 answers\r<BR>\n" );
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document.write( "thank you very much<BR>\n" );
document.write( "i hope you can help  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #853318 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(53570)</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=853318\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "i'm trying to show a=b or a=1/b without plugging in the values for a.<BR>\n" );
document.write( "this is the equation<BR>\n" );
document.write( "a+1/a=b+1/b<BR>\n" );
document.write( "i have tried multiplying both sides by ab<BR>\n" );
document.write( "i tried the quadratic equation but that didn't work very well cause i couldn't get the square root out<BR>\n" );
document.write( "i just need a step by step explanation of how to get there cause its driving me crazy and i think i'm just missing something simple<BR>\n" );
document.write( "please remember. i know how to substitute. i'm basically proving a= b,1/b<BR>\n" );
document.write( "which is why i tried making it a quadratic because i knew there were 2 answers<BR>\n" );
document.write( "thank you very much<BR>\n" );
document.write( "i hope you can help<BR>\n" );
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document.write( "Good question and good problem.\r<BR>\n" );
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document.write( "@mananth was on a right track, but his solution was incomplete.<BR>\n" );
document.write( "I came to present a complete solution/answer/exposition/explanation.\r<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "    a + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fa ALIGN=MIDDLE  ALT=\"1%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > = b + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fb ALIGN=MIDDLE  ALT=\"1%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r\n" );
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document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%5E2%2B1%29%2Fa ALIGN=MIDDLE  ALT=\"%28a%5E2%2B1%29%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b%5E2%2B1%29%2Fb%29 ALIGN=MIDDLE  ALT=\"%28b%5E2%2B1%29%2Fb%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r\n" );
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document.write( "multiply by ab\r\n" );
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document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2A%28a%5E2%2B1%29 ALIGN=MIDDLE  ALT=\"b%2A%28a%5E2%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2A%28b%5E2%2B1%29 ALIGN=MIDDLE  ALT=\"a%2A%28b%5E2%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r\n" );
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document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2Aa%5E2+%2B+b ALIGN=MIDDLE  ALT=\"b%2Aa%5E2+%2B+b\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ab%5E2%2Ba ALIGN=MIDDLE  ALT=\"ab%5E2%2Ba\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r\n" );
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document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ba%5E2+=+ab%5E2 ALIGN=MIDDLE  ALT=\"ba%5E2+=+ab%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = a - b\r\n" );
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document.write( "    ab(a-b)=(a-b)\r\n" );
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document.write( "    ab(a-b) - (a-b) = 0\r\n" );
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document.write( "    (ab-1)*(a-b) = 0\r\n" );
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document.write( "So, EITHER ab = 1,  which is the same as  a = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fb ALIGN=MIDDLE  ALT=\"1%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (one of the two your options) \r\n" );
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document.write( "    OR     a = b   (second of the two your options).\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "Solved completely.\r<BR>\n" );
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document.write( "My congrats !\r<BR>\n" );
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document.write( " </SPAN>\n" );
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