document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=79700>Question 79700</A>: <I><SPAN STYLE=\"word-break: break-all;\"> To solve 1/x-3+ 1/x+3 = 10/x^2-9, which step would result?\r<BR>\n" );
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document.write( "I got: (x+3)+(x+3) = 10\r<BR>\n" );
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document.write( "Is this correct?<BR>\n" );
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 #57206 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=57206\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28x-3%29+%2B++1%2F%28x%2B3%29+=+10%2F%28x%5E2-9%29 ALIGN=MIDDLE  ALT=\"1%2F%28x-3%29+%2B++1%2F%28x%2B3%29+=+10%2F%28x%5E2-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Don't think you are correct, but let's check your answer.  You got:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29%2B%28x%2B3%29+=+10 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%2B%28x%2B3%29+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Remove the parentheses and this becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+3++%2B+x+%2B+3+=+10 ALIGN=MIDDLE  ALT=\"x+%2B+3++%2B+x+%2B+3+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Add like terms on the left side and you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+%2B+6+=+10 ALIGN=MIDDLE  ALT=\"2x+%2B+6+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Subtract 6 from both sides and you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+=+4 ALIGN=MIDDLE  ALT=\"2x+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Then divide both sides by 2 and you finally have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2 ALIGN=MIDDLE  ALT=\"x+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  If you return to the<BR>\n" );
document.write( "original equation and substitute 2 for x it becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%282-3%29%2B1%2F%282%2B3%29+=+10%2F%282%5E2+-9%29 ALIGN=MIDDLE  ALT=\"1%2F%282-3%29%2B1%2F%282%2B3%29+=+10%2F%282%5E2+-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Doing the math in the 3 denominators results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28-1%29+%2B+1%2F5+=+10%2F%284-9%29 ALIGN=MIDDLE  ALT=\"1%2F%28-1%29+%2B+1%2F5+=+10%2F%284-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and this further simplifies to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1+%2B++1%2F5+=+10%2F-5 ALIGN=MIDDLE  ALT=\"-1+%2B++1%2F5+=+10%2F-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "which becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1+%2B+1%2F5+=+-2 ALIGN=MIDDLE  ALT=\"-1+%2B+1%2F5+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "by adding +1 to both sides this becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2B1%2F5+=+-1 ALIGN=MIDDLE  ALT=\"%2B1%2F5+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "That doesn't look too good.<BR>\n" );
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document.write( "Let's go back to the original problem and work it out:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28x-3%29+%2B++1%2F%28x%2B3%29+=+10%2F%28x%5E2-9%29 ALIGN=MIDDLE  ALT=\"1%2F%28x-3%29+%2B++1%2F%28x%2B3%29+=+10%2F%28x%5E2-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You probably recognized that the denominator on the right side factors to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%2A%28x%2B3%29 ALIGN=MIDDLE  ALT=\"%28x-3%29%2A%28x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Substitute that into the equation and it becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28x-3%29+%2B++1%2F%28x%2B3%29+=+10%2F%28%28x-3%29%28x%2B3%29%29 ALIGN=MIDDLE  ALT=\"1%2F%28x-3%29+%2B++1%2F%28x%2B3%29+=+10%2F%28%28x-3%29%28x%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now multiply all the terms on both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%28x%2B3%29 ALIGN=MIDDLE  ALT=\"%28x-3%29%28x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  When you do it becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x-3%29%28x%2B3%29%2A1%29%2F%28x-3%29+%2B+%28%28x-3%29%28x%2B3%29%2A1%29%2F%28x%2B3%29+=+%28%28x-3%29%28x%2B3%29%2A10%29%2F%28%28x-3%29%28x%2B3%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "cross out the common terms in the denominator and the numerator:<BR>\n" );
document.write( ".\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28cross%28x-3%29%28x%2B3%29%2A1%29%2Fcross%28x-3%29+%2B+%28%28x-3%29cross%28x%2B3%29%2A1%29%2Fcross%28x%2B3%29+=+%28cross%28x-3%29cross%28x%2B3%29%2A10%29%2F%28cross%28x-3%29cross%28x%2B3%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29+%2B+%28x-3%29+=+10 ALIGN=MIDDLE  ALT=\"%28x%2B3%29+%2B+%28x-3%29+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Remove the parentheses:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+3+%2B+x+-+3+=+10 ALIGN=MIDDLE  ALT=\"x+%2B+3+%2B+x+-+3+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Combine the like terms on the left side (note +3 -3 = 0) and you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+=+10 ALIGN=MIDDLE  ALT=\"2x+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Finally divide both sides by 2 and you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+5 ALIGN=MIDDLE  ALT=\"x+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now let's check the answer.  Return to the original equation and substitute 5 for x to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28x-3%29+%2B++1%2F%28x%2B3%29+=+10%2F%28x%5E2-9%29 ALIGN=MIDDLE  ALT=\"1%2F%28x-3%29+%2B++1%2F%28x%2B3%29+=+10%2F%28x%5E2-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%285-3%29+%2B++1%2F%285%2B3%29+=+10%2F%285%5E2-9%29 ALIGN=MIDDLE  ALT=\"1%2F%285-3%29+%2B++1%2F%285%2B3%29+=+10%2F%285%5E2-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2+%2B+1%2F8+=+10%2F%2825-9%29 ALIGN=MIDDLE  ALT=\"1%2F2+%2B+1%2F8+=+10%2F%2825-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F8+%2B+1%2F8+=+10%2F16 ALIGN=MIDDLE  ALT=\"4%2F8+%2B+1%2F8+=+10%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F8+=+10%2F16 ALIGN=MIDDLE  ALT=\"5%2F8+=+10%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F8+=+5%2F8 ALIGN=MIDDLE  ALT=\"5%2F8+=+5%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "That works ... so the answer is x = 5<BR>\n" );
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document.write( "Hope this helps you to find your mistake. </SPAN>\n" );
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