document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=168278>Question 168278</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0321269470/algebrahomeworkh>Introductory Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> (3a-5)/(a^2+4a+3)+(2a+2)/(a+3)=(a-3)/(a+1)\r<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 #124052 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=124052\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%283a-5%29%29%2F%28%28a%5E2%2B4a%2B3%29%29 ALIGN=MIDDLE  ALT=\"%28%283a-5%29%29%2F%28%28a%5E2%2B4a%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%282a%2B2%29%29%2F%28%28a%2B3%29%29 ALIGN=MIDDLE  ALT=\"%28%282a%2B2%29%29%2F%28%28a%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28a-3%29%29%2F%28%28a%2B1%29%29 ALIGN=MIDDLE  ALT=\"%28%28a-3%29%29%2F%28%28a%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Factor where we can:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%283a-5%29%29%2F%28%28a%2B3%29%28a%2B1%29%29 ALIGN=MIDDLE  ALT=\"%28%283a-5%29%29%2F%28%28a%2B3%29%28a%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%28a%2B1%29%29%2F%28%28a%2B3%29%29 ALIGN=MIDDLE  ALT=\"%282%28a%2B1%29%29%2F%28%28a%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28a-3%29%29%2F%28%28a%2B1%29%29 ALIGN=MIDDLE  ALT=\"%28%28a-3%29%29%2F%28%28a%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Multiply equation by (a+3)(x+1)<BR>\n" );
document.write( "(a+3)(a+1)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%283a-5%29%29%2F%28%28a%2B3%29%28a%2B1%29%29 ALIGN=MIDDLE  ALT=\"%28%283a-5%29%29%2F%28%28a%2B3%29%28a%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + (a+3)(a+1)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%28a%2B1%29%29%2F%28%28a%2B3%29%29 ALIGN=MIDDLE  ALT=\"%282%28a%2B1%29%29%2F%28%28a%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = (a+3)(a+1)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28a-3%29%29%2F%28%28a%2B1%29%29 ALIGN=MIDDLE  ALT=\"%28%28a-3%29%29%2F%28%28a%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Cancel out the denominators and you have:<BR>\n" );
document.write( "(3a-5) + 2(a+1)(a+1) = (a+3)(a-3)<BR>\n" );
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document.write( "FOIL<BR>\n" );
document.write( "(3a - 5) + 2(a^2 + 2a + 1) = a^2 - 9<BR>\n" );
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document.write( "3a - 5 + 2a^2 + 4a + 2 = a^2 - 9<BR>\n" );
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document.write( "Combine like terms on the left:<BR>\n" );
document.write( "2a^2 - a^2 + 3a + 4a - 5 + 2 + 9 = 0<BR>\n" );
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document.write( "a^2 + 7a + 6 = 0<BR>\n" );
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document.write( "Factor this to:<BR>\n" );
document.write( "(a + 6)(a + 1) = 0<BR>\n" );
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document.write( "a = -6<BR>\n" );
document.write( "and <BR>\n" );
document.write( "a = -1<BR>\n" );
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document.write( "Check solution of x=-6 in original equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%283%28-6%29-5%29%29%2F%28%28-6%5E2%2B4%28-6%29%2B3%29%29 ALIGN=MIDDLE  ALT=\"%28%283%28-6%29-5%29%29%2F%28%28-6%5E2%2B4%28-6%29%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%282%28-6%29%2B2%29%29%2F%28%28-6%2B3%29%29 ALIGN=MIDDLE  ALT=\"%28%282%28-6%29%2B2%29%29%2F%28%28-6%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28-6-3%29%29%2F%28%28-6%2B1%29%29 ALIGN=MIDDLE  ALT=\"%28%28-6-3%29%29%2F%28%28-6%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Do the math, find the common denominator, and you have;<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-23%2F15 ALIGN=MIDDLE  ALT=\"-23%2F15\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50%2F15 ALIGN=MIDDLE  ALT=\"50%2F15\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=27%2F15 ALIGN=MIDDLE  ALT=\"27%2F15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( " x=-1 can not be a solution, note that in the last denominator we have division by 0 </SPAN>\n" );
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