document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=547547>Question 547547</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Help solve please: 3/2x - x/4x^2-1 = 7/4x+2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #356927 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=356927\">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=+3%2F2x ALIGN=MIDDLE  ALT=\"+3%2F2x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-+x%2F4x%5E2 ALIGN=MIDDLE  ALT=\"+-+x%2F4x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1+=+7%2F4x%2B2 ALIGN=MIDDLE  ALT=\"-1+=+7%2F4x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >? That would be way to simple.<BR>\n" );
document.write( "You probably meant 3/2x - x/(4x^2-1) = 7/(4x+2), which I can write as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F2x+-+x%2F%284x%5E2-1%29+=+7%2F%284x%2B2%29 ALIGN=MIDDLE  ALT=\"3%2F2x+-+x%2F%284x%5E2-1%29+=+7%2F%284x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The first thing to do is looking for factors in the denominators. I can factor them, to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F2x+-+x%2F%28%282x-1%29%282x%2B1%29%29+=+7%2F%282%282x%2B1%29%29 ALIGN=MIDDLE  ALT=\"3%2F2x+-+x%2F%28%282x-1%29%282x%2B1%29%29+=+7%2F%282%282x%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "A good common denominator would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%282x-1%29%282x%2B1%29 ALIGN=MIDDLE  ALT=\"2x%282x-1%29%282x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, but instead of writing denominators over and over I will multiply both sides of the equation by that expression to eliminate denominators.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Across%282x%29%282x-1%29%282x%2B1%29%2Fcross%282x%29+-+x%2A2x%2Across%28%282x-1%29%282x%2B1%29%29%2Fcross%28%282x-1%29%282x%2B1%29%29+=+7%2Across%282%29%2Ax%2A%282x-1%29%2Across%282x%2B1%29%2F%28cross%282%29%2Across%282x%2B1%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >, which simplifies to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A%282x-1%29%282x%2B1%29+-+x%2A2x+=+7%2Ax%2A%282x-1%29 ALIGN=MIDDLE  ALT=\"3%2A%282x-1%29%282x%2B1%29+-+x%2A2x+=+7%2Ax%2A%282x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiplying as indicated, we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12x%5E2-3+-+2x%5E2+=+14x%5E2-7x ALIGN=MIDDLE  ALT=\"12x%5E2-3+-+2x%5E2+=+14x%5E2-7x\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x%5E2-1+=+14x%5E2-7x ALIGN=MIDDLE  ALT=\"10x%5E2-1+=+14x%5E2-7x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Adding <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3-10x%5E2 ALIGN=MIDDLE  ALT=\"3-10x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides, we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=4x%5E2-7x%2B3 ALIGN=MIDDLE  ALT=\"0=4x%5E2-7x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Whichever way you solve that quadratic equation (factoring, completing the square, or applying the quadratic formula), you get the two solutions<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3%2F4 ALIGN=MIDDLE  ALT=\"x=3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "It's a good idea to check, because, even if we make no mistakes, on eliminating denominators we can introduce extraneous solutions, that were not solutions of the original equation because they made one of the denominators zero. Our solutions do not make any of the denominators zero, but I often make mistakes, so I'll verify the solutions.<BR>\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F2x+-+x%2F%284x%5E2-1%29+=3%2F%282%2A1%29+-+1%2F%284%2A1%5E2-1%29=3%2F2-1%2F3=7%2F6 ALIGN=MIDDLE  ALT=\"3%2F2x+-+x%2F%284x%5E2-1%29+=3%2F%282%2A1%29+-+1%2F%284%2A1%5E2-1%29=3%2F2-1%2F3=7%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F%284x%2B2%29=7%2F%284%2A1%2B2%29=7%2F6 ALIGN=MIDDLE  ALT=\"7%2F%284x%2B2%29=7%2F%284%2A1%2B2%29=7%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3%2F4 ALIGN=MIDDLE  ALT=\"x=3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F2x+-+x%2F%284x%5E2-1%29+=3%2F%282%2A%283%2F4%29%29+-+%283%2F4%29%2F%284%2A%283%2F4%29%5E2-1%29=3%2F%283%2F2%29-%283%2F4%29%2F%289%2F4-1%29=2-%283%2F4%29%2F%285%2F4%29=2-3%2F5=7%2F5 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F%284x%2B2%29=7%2F%284%2A%283%2F4%29%2B2%29=7%2F%283%2B2%29=7%2F5 ALIGN=MIDDLE  ALT=\"7%2F%284x%2B2%29=7%2F%284%2A%283%2F4%29%2B2%29=7%2F%283%2B2%29=7%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Both solutions work. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );