document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=190424>Question 190424</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hey, I'm needing some help checking this problem for an exam review:\r<BR>\n" );
document.write( "\n" );
document.write( "Solve the equation:\r<BR>\n" );
document.write( "\n" );
document.write( "(5/a) - (7)/(a+1) = (a^2 - 2a + 4)/(a^2 + a)\r<BR>\n" );
document.write( "\n" );
document.write( "thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #142983 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=142983\">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=5%2Fa+-+7%2F%28a%2B1%29+=+%28a%5E2+-+2a+%2B+4%29%2F%28a%5E2+%2B+a%29+ ALIGN=MIDDLE  ALT=\"5%2Fa+-+7%2F%28a%2B1%29+=+%28a%5E2+-+2a+%2B+4%29%2F%28a%5E2+%2B+a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation. \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=5%2Fa+-+7%2F%28a%2B1%29+=+%28a%5E2+-+2a+%2B+4%29%2F%28a%28a+%2B+1%29%29+ ALIGN=MIDDLE  ALT=\"5%2Fa+-+7%2F%28a%2B1%29+=+%28a%5E2+-+2a+%2B+4%29%2F%28a%28a+%2B+1%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor the last denominator\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So we can see that the LCD is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%28a%2B1%29 ALIGN=MIDDLE  ALT=\"a%28a%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Take note that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%3C%3E0 ALIGN=MIDDLE  ALT=\"a%3C%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%3C%3E-1 ALIGN=MIDDLE  ALT=\"a%3C%3E-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > (these values cause a division by zero)\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=cross%28a%29%28a%2B1%29%285%2Fcross%28a%29%29+-+a%2Across%28%28a%2B1%29%29%287%2Fcross%28%28a%2B1%29%29%29+=+cross%28a%28a%2B1%29%29%28a%5E2+-+2a+%2B+4%29%2F%28cross%28a%28a%2B1%29%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply EVERY term by the LCD <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%28a%2B1%29 ALIGN=MIDDLE  ALT=\"a%28a%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to clear the fractions\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=5%28a%2B1%29-7a=a%5E2+-+2a+%2B+4 ALIGN=MIDDLE  ALT=\"5%28a%2B1%29-7a=a%5E2+-+2a+%2B+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > 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=5a%2B5-7a=a%5E2+-+2a+%2B+4 ALIGN=MIDDLE  ALT=\"5a%2B5-7a=a%5E2+-+2a+%2B+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\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=5-2a=a%5E2+-+2a+%2B+4 ALIGN=MIDDLE  ALT=\"5-2a=a%5E2+-+2a+%2B+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like 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=0=a%5E2+-+2a+%2B+4-5%2B2a ALIGN=MIDDLE  ALT=\"0=a%5E2+-+2a+%2B+4-5%2B2a\"   DISABLED_style= \"max-width:90%; height:auto;\" > Get all of the terms to the right side.\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=0=a%5E2+-+1 ALIGN=MIDDLE  ALT=\"0=a%5E2+-+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like 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=0=%28a%2B1%29%28a-1%29 ALIGN=MIDDLE  ALT=\"0=%28a%2B1%29%28a-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor\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=a%2B1=0 ALIGN=MIDDLE  ALT=\"a%2B1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a-1=0 ALIGN=MIDDLE  ALT=\"a-1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Set each factor equal to zero\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=a=-1 ALIGN=MIDDLE  ALT=\"a=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Solve each equation\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Remember, our original restrictions are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%3C%3E0 ALIGN=MIDDLE  ALT=\"a%3C%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%3C%3E-1 ALIGN=MIDDLE  ALT=\"a%3C%3E-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-1 ALIGN=MIDDLE  ALT=\"a=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > is NOT a solution\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So the only solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );