document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=95841>Question 95841</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Perform the indicated operation.  Simplify if possible\r<BR>\n" );
document.write( "\n" );
document.write( "5x/x^2-7x+10  -  10/x^2-7x+10 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #69827 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=69827\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given to simplify:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285x%2F%28x%5E2-7x%2B10%29%29++-++%2810%2F%28x%5E2-7x%2B10%29%29 ALIGN=MIDDLE  ALT=\"%285x%2F%28x%5E2-7x%2B10%29%29++-++%2810%2F%28x%5E2-7x%2B10%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Notice that the two fractions have a common denominator. Therefore their numerators <BR>\n" );
document.write( "can be combined over the common denominator. When you do that the given polynomial becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285x+-+10%29%2F%28x%5E2+-7x+%2B+10%29 ALIGN=MIDDLE  ALT=\"%285x+-+10%29%2F%28x%5E2+-7x+%2B+10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Next notice that in the numerator both terms have a common factor of 5. So factor the numerator<BR>\n" );
document.write( "and the polynomial then becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%28x+-+2%29%29%2F%28x%5E2+-7x%2B10%29 ALIGN=MIDDLE  ALT=\"%285%28x+-+2%29%29%2F%28x%5E2+-7x%2B10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Then observe that the denominator can be factored to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+5%29%28x-2%29 ALIGN=MIDDLE  ALT=\"%28x+-+5%29%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Substitute this<BR>\n" );
document.write( "factored form for the denominator and you have:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%28x-2%29%29%2F%28%28x-5%29%28x-2%29%29 ALIGN=MIDDLE  ALT=\"%285%28x-2%29%29%2F%28%28x-5%29%28x-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "There is a common term in the denominator and the numerator. Cancel this common term:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%28cross%28x-2%29%29%29%2F%28%28x-5%29%28cross%28x-2%29%29%29 ALIGN=MIDDLE  ALT=\"%285%28cross%28x-2%29%29%29%2F%28%28x-5%29%28cross%28x-2%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "and you are left with the simplified form:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F%28x-5%29 ALIGN=MIDDLE  ALT=\"5%2F%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "No further simplification is needed. This is your answer.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Hope this helps you to understand the problem and how to work it.<BR>\n" );
document.write( ". </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );