document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=239034>Question 239034</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The whole rational equations has me stumped!  Can you please help with this one?\r<BR>\n" );
document.write( "\n" );
document.write( "Solve...\r<BR>\n" );
document.write( "\n" );
document.write( "3a-5/a^2+4a+3 + 2a+2/a+3 = a-3/a+1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #175585 by </B><A HREF=/tutors/aboutme.mpl?userid=College+Student><B>College Student(505)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=College+Student><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/cgi-bin/show-face.mpl?user=College+Student><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=175585\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Problem:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%283a-5%29%2F%28a%5E2%2B4a%2B3%29%29%2B%28%282a%2B2%29%2F%28a%2B3%29%29=%28a-3%29%2F%28a%2B1%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "It took me several steps to solve this problem.  Look carefully as you move through the steps.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "First make eqn equal to zero:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%283a-5%29%2F%28a%5E2%2B4a%2B3%29%29%2B%28%282a%2B2%29%2F%28a%2B3%29%29-%28%28a-3%29%2F%28a%2B1%29%29=0 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now factor first denominator:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%283a-5%29%2F%28%28a%2B3%29%28a%2B1%29%29%29%2B%28%282a%2B2%29%2F%28a%2B3%29%29-%28%28a-3%29%2F%28a%2B1%29%29=0 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I would also factor the second numerator.  You'll know why in a moment... it'll make our lives easier.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%283a-5%29%2F%28%28a%2B3%29%28a%2B1%29%29%29%2B%28%282%28a%2B1%29%29%2F%28a%2B3%29%29-%28%28a-3%29%2F%28a%2B1%29%29=0 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "* In order to add fractions, we need common denominators, right?<BR>\n" );
document.write( "* We also know that any number multiplied by 1 is equal to itself, in other words, it doesn't change the original value.<BR>\n" );
document.write( "* Furthermore, we know that any number divided by itself is equal to 1, right?<BR>\n" );
document.write( "* So, in order to have equal denominators, we need to multiply the second fraction by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2B1%29%2F%28a%2B1%29 ALIGN=MIDDLE  ALT=\"%28a%2B1%29%2F%28a%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the third denominator by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2B3%29%2F%28a%2B3%29 ALIGN=MIDDLE  ALT=\"%28a%2B3%29%2F%28a%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "* This is how the new equation would look like:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%283a-5%29%2F%28%28a%2B3%29%28a%2B1%29%29%29%2B%28%282%28a%2B1%29%29%2F%28a%2B3%29%29%28%28a%2B1%29%2F%28a%2B1%29%29-%28%28a-3%29%2F%28a%2B1%29%29%28%28a%2B3%29%2F%28a%2B3%29%29=0 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now in a more cohesive way:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283a-5%29%2F%28%28a%2B3%29%28a%2B1%29%29%2B%282%28a%2B1%29%28a%2B1%29%29%2F%28%28a%2B3%29%28a%2B1%29%29-%28%28a-3%29%28a%2B3%29%29%2F%28%28a%2B1%29%28a%2B3%29%29=0 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since we now have the same denominator, we can group all numerators above one common denominator.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%283a-5%29%2B2%28a%2B1%29%28a%2B1%29-%28%28a-3%29%28a%2B3%29%29%29%2F%28%28a%2B1%29%28a%2B3%29%29=0 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now perform multiplications, leave denominator as is.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%283a-5%29%2B%282%28a%5E2%2B2a%2B1%29%29-%28a%5E2-9%29%29%2F%28%28a%2B1%29%28a%2B3%29%29=0 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Distribute the negative sign in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28a%5E2-9%29 ALIGN=MIDDLE  ALT=\"-%28a%5E2-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%283a-5%29%2B%282%28a%5E2%2B2a%2B1%29%29%2B%28-a%5E2%2B9%29%29%2F%28%28a%2B1%29%28a%2B3%29%29=0 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply the 2 in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28a%5E2%2B2a%2B1%29 ALIGN=MIDDLE  ALT=\"2%28a%5E2%2B2a%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283a-5%2B2a%5E2%2B4a%2B2-a%5E2%2B9%29%2F%28%28a%2B1%29%28a%2B3%29%29=0 ALIGN=MIDDLE  ALT=\"%283a-5%2B2a%5E2%2B4a%2B2-a%5E2%2B9%29%2F%28%28a%2B1%29%28a%2B3%29%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Combine like terms:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283a%2B4a-5%2B2%2B9%2B2a%5E2-a%5E2%29%2F%28%28a%2B1%29%28a%2B3%29%29=0 ALIGN=MIDDLE  ALT=\"%283a%2B4a-5%2B2%2B9%2B2a%5E2-a%5E2%29%2F%28%28a%2B1%29%28a%2B3%29%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287a%2B6%2Ba%5E2%29%2F%28%28a%2B1%29%28a%2B3%29%29=0 ALIGN=MIDDLE  ALT=\"%287a%2B6%2Ba%5E2%29%2F%28%28a%2B1%29%28a%2B3%29%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "Now in standard form to make it easier to factor: <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%5E2%2B7a%2B6%29%2F%28%28a%2B1%29%28a%2B3%29%29=0 ALIGN=MIDDLE  ALT=\"%28a%5E2%2B7a%2B6%29%2F%28%28a%2B1%29%28a%2B3%29%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28a%2B6%29%28a%2B3%29%29%2F%28%28a%2B1%29%28a%2B3%29%29=0 ALIGN=MIDDLE  ALT=\"%28%28a%2B6%29%28a%2B3%29%29%2F%28%28a%2B1%29%28a%2B3%29%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now simplify and you're done.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2B6%29%2F%28a%2B1%29 ALIGN=MIDDLE  ALT=\"%28a%2B6%29%2F%28a%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "It's a long problem.  I hope you understood it and were able to follow it. :) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );