document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=72062>Question 72062</A>: <I><SPAN STYLE=\"word-break: break-all;\"> answer for this problem x+7/x=8 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #51521 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=51521\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since the heading on your problem indicates you are working on quadratic equations,<BR>\n" );
document.write( "I interpret your problem as being:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+7%2Fx+=+8 ALIGN=MIDDLE  ALT=\"x+%2B+7%2Fx+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You can convert this to a quadratic equation by multiplying both sides of this equation<BR>\n" );
document.write( "by x to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+7+=+8x ALIGN=MIDDLE  ALT=\"x%5E2+%2B+7+=+8x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Then subtract 8x from both sides to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+8x+%2B+7+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-+8x+%2B+7+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This could be solved using the quadratic formula, but it is easier to solve this by noting<BR>\n" );
document.write( "that this quadratic equation factors into:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+7%29%2A%28x+-+1%29+=+0 ALIGN=MIDDLE  ALT=\"%28x+-+7%29%2A%28x+-+1%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "(You can check by multiplying <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-7%29%2A%28x-1%29 ALIGN=MIDDLE  ALT=\"%28x-7%29%2A%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and satisfy yourself that the result is <BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+8x+%2B+7 ALIGN=MIDDLE  ALT=\"x%5E2+-+8x+%2B+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This equation will be true if either of the factors equals zero because any multiplier<BR>\n" );
document.write( "that equals zero on the left side causes the entire left side to be zero and that makes<BR>\n" );
document.write( "it equal to the right side.<BR>\n" );
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document.write( "So, all we need to do is solve:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+7+=+0 ALIGN=MIDDLE  ALT=\"x+-+7+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and <BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+1+=+0 ALIGN=MIDDLE  ALT=\"x+-+1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The two solutions to these equations are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2B7 ALIGN=MIDDLE  ALT=\"x+=+%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2B1 ALIGN=MIDDLE  ALT=\"x+=+%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and these two values<BR>\n" );
document.write( "for x will each satisfy the quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+8x+%2B+7+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-+8x+%2B+7+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "Hope this helps you to understand how to do quadratic equations that can be factored.<BR>\n" );
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