document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=136242>Question 136242</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi could you help me solve this rational equation?\r<BR>\n" );
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document.write( "y-3/5 = y+1/7\r<BR>\n" );
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document.write( "thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #99784 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=99784\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I have to assume that you meant:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-3%29%2F5=%28y%2B1%29%2F7 ALIGN=MIDDLE  ALT=\"%28y-3%29%2F5=%28y%2B1%29%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >, because what you wrote:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-3%2F5=y%2B1%2F7 ALIGN=MIDDLE  ALT=\"y-3%2F5=y%2B1%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > has no solution.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-3%29%2F5=%28y%2B1%29%2F7 ALIGN=MIDDLE  ALT=\"%28y-3%29%2F5=%28y%2B1%29%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "7 and 5 have no common factors so the LCD is 7*5=35, so:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%28y-3%29%2F35=5%28y%2B1%29%2F35 ALIGN=MIDDLE  ALT=\"7%28y-3%29%2F35=5%28y%2B1%29%2F35\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Add the additive inverse of the right side to both sides:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%28y-3%29%2F35-5%28y%2B1%29%2F35=0 ALIGN=MIDDLE  ALT=\"7%28y-3%29%2F35-5%28y%2B1%29%2F35=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since both fractions have the same denominator, add the numerators directly:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287%28y-3%29-5%28y%2B1%29%29%2F35=0 ALIGN=MIDDLE  ALT=\"%287%28y-3%29-5%28y%2B1%29%29%2F35=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Distribute and collect like terms:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282y-26%29%2F35=0 ALIGN=MIDDLE  ALT=\"%282y-26%29%2F35=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Fb=0 ALIGN=MIDDLE  ALT=\"a%2Fb=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > if and only if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=0 ALIGN=MIDDLE  ALT=\"a=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%3C%3E0 ALIGN=MIDDLE  ALT=\"b%3C%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  The denominator is not a problem because clearly <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35%3C%3E0 ALIGN=MIDDLE  ALT=\"35%3C%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so all we need do is set the numerator equal to zero and solve:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y-26=0 ALIGN=MIDDLE  ALT=\"2y-26=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y=26 ALIGN=MIDDLE  ALT=\"2y=26\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=13 ALIGN=MIDDLE  ALT=\"y=13\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2813-3%29%2F5=%2813%2B1%29%2F7 ALIGN=MIDDLE  ALT=\"%2813-3%29%2F5=%2813%2B1%29%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2F5=14%2F7 ALIGN=MIDDLE  ALT=\"10%2F5=14%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2=2 ALIGN=MIDDLE  ALT=\"2=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, Answer checks.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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