document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=274297>Question 274297</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi. I'm trying to solve 2xy+5x-2y-5 over 3xy+4x-3y-4. Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #200197 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=200197\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The key to this problem is factoring\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let's factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2xy%2B5x-2y-5 ALIGN=MIDDLE  ALT=\"2xy%2B5x-2y-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2xy%2B5x-2y-5 ALIGN=MIDDLE  ALT=\"2xy%2B5x-2y-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282xy%2B5x%29%2B%28-2y-5%29 ALIGN=MIDDLE  ALT=\"%282xy%2B5x%29%2B%28-2y-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Group the terms.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%282y%2B5%29%2B%28-2y-5%29 ALIGN=MIDDLE  ALT=\"x%282y%2B5%29%2B%28-2y-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the GCF 'x' from the first group.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%282y%2B5%29-%282y%2B5%29 ALIGN=MIDDLE  ALT=\"x%282y%2B5%29-%282y%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the GCF -1 from the second group.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%282y%2B5%29 ALIGN=MIDDLE  ALT=\"%28x-1%29%282y%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the GCF <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y%2B4 ALIGN=MIDDLE  ALT=\"3y%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > from the entire expression.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2xy%2B5x-2y-5 ALIGN=MIDDLE  ALT=\"2xy%2B5x-2y-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%282y%2B5%29 ALIGN=MIDDLE  ALT=\"%28x-1%29%282y%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "--------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now let's factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3xy%2B4x-3y-4 ALIGN=MIDDLE  ALT=\"3xy%2B4x-3y-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3xy%2B4x-3y-4 ALIGN=MIDDLE  ALT=\"3xy%2B4x-3y-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283xy%2B4x%29%2B%28-3y-4%29 ALIGN=MIDDLE  ALT=\"%283xy%2B4x%29%2B%28-3y-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Group the terms.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%283y%2B4%29%2B%28-3y-4%29 ALIGN=MIDDLE  ALT=\"x%283y%2B4%29%2B%28-3y-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the GCF 'x' from the first group.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%283y%2B4%29-%283y%2B4%29 ALIGN=MIDDLE  ALT=\"x%283y%2B4%29-%283y%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Factor out the GCF -1 from the second group.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%283y%2B4%29 ALIGN=MIDDLE  ALT=\"%28x-1%29%283y%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the GCF <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y%2B4 ALIGN=MIDDLE  ALT=\"3y%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > from the entire expression.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3xy%2B4x-3y-4 ALIGN=MIDDLE  ALT=\"3xy%2B4x-3y-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%283y%2B4%29 ALIGN=MIDDLE  ALT=\"%28x-1%29%283y%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now that we have the factorizations, we can now simplify:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282xy%2B5x-2y-5%29%2F%283xy%2B4x-3y-4%29 ALIGN=MIDDLE  ALT=\"%282xy%2B5x-2y-5%29%2F%283xy%2B4x-3y-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x-1%29%282y%2B5%29%29%2F%283xy%2B4x-3y-4%29 ALIGN=MIDDLE  ALT=\"%28%28x-1%29%282y%2B5%29%29%2F%283xy%2B4x-3y-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor the numerator (see the first factorization above)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x-1%29%282y%2B5%29%29%2F%28%28x-1%29%283y%2B4%29%29 ALIGN=MIDDLE  ALT=\"%28%28x-1%29%282y%2B5%29%29%2F%28%28x-1%29%283y%2B4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor the denominator (see the second factorization above)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28highlight%28%28x-1%29%29%282y%2B5%29%29%2F%28highlight%28%28x-1%29%29%283y%2B4%29%29 ALIGN=MIDDLE  ALT=\"%28highlight%28%28x-1%29%29%282y%2B5%29%29%2F%28highlight%28%28x-1%29%29%283y%2B4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Highlight the common terms.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28cross%28%28x-1%29%29%282y%2B5%29%29%2F%28cross%28%28x-1%29%29%283y%2B4%29%29 ALIGN=MIDDLE  ALT=\"%28cross%28%28x-1%29%29%282y%2B5%29%29%2F%28cross%28%28x-1%29%29%283y%2B4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Cancel out the common terms.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282y%2B5%29%2F%283y%2B4%29 ALIGN=MIDDLE  ALT=\"%282y%2B5%29%2F%283y%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282xy%2B5x-2y-5%29%2F%283xy%2B4x-3y-4%29 ALIGN=MIDDLE  ALT=\"%282xy%2B5x-2y-5%29%2F%283xy%2B4x-3y-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282y%2B5%29%2F%283y%2B4%29 ALIGN=MIDDLE  ALT=\"%282y%2B5%29%2F%283y%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "In other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282xy%2B5x-2y-5%29%2F%283xy%2B4x-3y-4%29=%282y%2B5%29%2F%283y%2B4%29 ALIGN=MIDDLE  ALT=\"%282xy%2B5x-2y-5%29%2F%283xy%2B4x-3y-4%29=%282y%2B5%29%2F%283y%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Note: One thing to point out is that the value of 'x' does not affect the final outcome of the expression since the 'x' terms cancel out. This isn't so obvious when you look at the original expression, but it becomes clear when we reach the last step. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );