document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=526830>Question 526830</A>: <I><SPAN STYLE=\"word-break: break-all;\"> hello I am having a hard time solving this equation, and would appreciate it if you would help me solve this problem:\r<BR>\n" );
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document.write( "1   1      1<BR>\n" );
document.write( "- + -   =  -<BR>\n" );
document.write( "x   x+3    4\r<BR>\n" );
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document.write( "I tried to rearrange numbers to eliminate fractions and got <BR>\n" );
document.write( "and got 4 = 2x + 3<BR>\n" );
document.write( "         1 = 2x<BR>\n" );
document.write( "        <BR>\n" );
document.write( "         1 <BR>\n" );
document.write( "         - = x<BR>\n" );
document.write( "         2<BR>\n" );
document.write( "I am really struggling solving quadratic problems involving fractions. Wondering if you may have any tips or suggestions. Thank you in advance. -Shae\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 #348708 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=348708\">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=1%2Fx+%2B+1%2F%28x%2B3%29+=+1%2F4 ALIGN=MIDDLE  ALT=\"1%2Fx+%2B+1%2F%28x%2B3%29+=+1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "trick is to multiply both sides by a common denominator 4x(x+3) to rid ourselves of all the denominators:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Multiplying both sides by 4x(x+3) we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28x%2B3%29+%2B+4x+=+x%28x%2B3%29 ALIGN=MIDDLE  ALT=\"4%28x%2B3%29+%2B+4x+=+x%28x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B12+%2B+4x+=+x%5E2%2B3x ALIGN=MIDDLE  ALT=\"4x%2B12+%2B+4x+=+x%5E2%2B3x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%2B12+=+x%5E2%2B3x ALIGN=MIDDLE  ALT=\"8x%2B12+=+x%5E2%2B3x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12+=+x%5E2-5x ALIGN=MIDDLE  ALT=\"12+=+x%5E2-5x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+x%5E2-5x-12 ALIGN=MIDDLE  ALT=\"0+=+x%5E2-5x-12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "since we can't factor, we apply the quadratic formula to get:<BR>\n" );
document.write( "x = {6.772, -1.772}<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Details of quadratic formula follows:<BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic.solver>SOLVE quadratic equation with variable</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B-5x%2B-12+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-5x%2B-12+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%28-5%29%5E2-4%2A1%2A-12=73 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-5%29%5E2-4%2A1%2A-12=73\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=73 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28--5%2B-sqrt%28+73+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--5%2B-sqrt%28+73+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%28-5%29%2Bsqrt%28+73+%29%29%2F2%5C1+=+6.77200187265877 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-5%29%2Bsqrt%28+73+%29%29%2F2%5C1+=+6.77200187265877\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%28-5%29-sqrt%28+73+%29%29%2F2%5C1+=+-1.77200187265877 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-5%29-sqrt%28+73+%29%29%2F2%5C1+=+-1.77200187265877\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B-5x%2B-12 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-5x%2B-12\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B-5x%2B-12+=+1%28x-6.77200187265877%29%2A%28x--1.77200187265877%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-5x%2B-12+=+1%28x-6.77200187265877%29%2A%28x--1.77200187265877%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 6.77200187265877, -1.77200187265877.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-5%2Ax%2B-12+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-5%2Ax%2B-12+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "</TD></TR></TABLE>\n" );