document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=69677>Question 69677</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (x/5x+10)+((x-3)/(x+2))=7/5\r<BR>\n" );
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document.write( "Solve for x<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #49619 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=49619\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "You are given:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F%285x%2B10%29+%2B+%28x-3%29%2F%28x%2B2%29+=+7%2F5 ALIGN=MIDDLE  ALT=\"x%2F%285x%2B10%29+%2B+%28x-3%29%2F%28x%2B2%29+=+7%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Notice that 5x + 10 can be factored by removing a 5 to make it 5(x+2).  If you do this the equation becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F5%28x%2B2%29+%2B+%28x-3%29%2F%28x%2B2%29+=+7%2F5 ALIGN=MIDDLE  ALT=\"x%2F5%28x%2B2%29+%2B+%28x-3%29%2F%28x%2B2%29+=+7%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Next you need to make all the denominators the same.  The common denominator is 5(x+2) so you don't need to do anything to the first term.  It already has the common denominator.  The second term <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%2F%28x%2B2%29 ALIGN=MIDDLE  ALT=\"%28x-3%29%2F%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > lacks a 5 in the denominator.  Therefore, multiply this term by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F5 ALIGN=MIDDLE  ALT=\"5%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  This is equivalent to multiplying the second term by 1 because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F5 ALIGN=MIDDLE  ALT=\"5%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > is 1.  When you do this the equation becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F5%28x%2B2%29+%2B+5%28x-3%29%2F5%28x%2B2%29+=+7%2F5 ALIGN=MIDDLE  ALT=\"x%2F5%28x%2B2%29+%2B+5%28x-3%29%2F5%28x%2B2%29+=+7%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Finally, on the right side of the equation the denominator lacks the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2 ALIGN=MIDDLE  ALT=\"x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Therefore, multiply the right side by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29%2F%28x%2B2%29 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%2F%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > [effectively multiplying it by 1.  When you do that the equation becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F5%28x%2B2%29+%2B+5%28x-3%29%2F5%28x%2B2%29+=+7%28x%2B2%29%2F5%28x%2B2%29 ALIGN=MIDDLE  ALT=\"x%2F5%28x%2B2%29+%2B+5%28x-3%29%2F5%28x%2B2%29+=+7%28x%2B2%29%2F5%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now you can get rid of the common denominator entirely by multiplying all the terms in the equation by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%28x%2B2%29 ALIGN=MIDDLE  ALT=\"5%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  This cancels out the denominator and leaves you with the equation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%2B+5%28x-3%29+=+7%28x%2B2%29 ALIGN=MIDDLE  ALT=\"+x+%2B+5%28x-3%29+=+7%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Its all downhill from here.  Just do the distributive multiplication on both sides to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+5x+-+15+=+7x%2B14 ALIGN=MIDDLE  ALT=\"x+%2B+5x+-+15+=+7x%2B14\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Add the two terms containing x on the left side to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x+-+15+=+7x+%2B+14 ALIGN=MIDDLE  ALT=\"6x+-+15+=+7x+%2B+14\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Add 15 to both sides:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x+=+7x+%2B+29 ALIGN=MIDDLE  ALT=\"6x+=+7x+%2B+29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Subtract 7x 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+=+29 ALIGN=MIDDLE  ALT=\"-x+=+29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Multiply both sides by -1:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-29 ALIGN=MIDDLE  ALT=\"x+=+-29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If you substitute this value for x in the original equation, you should find that it makes the left side of the equation equal to<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F5 ALIGN=MIDDLE  ALT=\"7%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Hope this helps. </SPAN>\n" );
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