document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=550677>Question 550677</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have a few problems with a worksheet I am doing, that do not understand can you please help me?<BR>\n" );
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document.write( "#1# Find the LCD of the fractions in the equation 4.5x / 2x+5 = 2x / x^2\r<BR>\n" );
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document.write( "I keep getting the answer (2x+5)(x) But it does not seem correct to me. <BR>\n" );
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document.write( "#2# Solve each equation if no real answer then select no real answer.\r<BR>\n" );
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document.write( "x / x-5 = -2x/x\r<BR>\n" );
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document.write( "I keep getting x=10 in every way I try to solve the problem and it is not listed as one of the possible answers, I marked no real solution.<BR>\n" );
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document.write( "#3# For this problem I do not understand on how to attempt it.\r<BR>\n" );
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document.write( "Find the focal length of the magnifying glass if you can see the butterfly clearly when your eye is 5.5 cm away from the glass and the glass is 25 cm away from the butterfly. The formula is 1/s + 1/t = 1/f.\r<BR>\n" );
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document.write( "I do not understand on how to do it.\r<BR>\n" );
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document.write( "#4# Simplify the rational equations.\r<BR>\n" );
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document.write( "x+5 / 3x+15 \r<BR>\n" );
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document.write( "I think it is in the simplist form already but I know you can divide the 5 into the 15 but can't divide the 3x into 3 .\r<BR>\n" );
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document.write( "x+5/4 divided by (x^2+5x)\r<BR>\n" );
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document.write( "I got 1/4x but i do not think it is correct.\r<BR>\n" );
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document.write( "#5#<BR>\n" );
document.write( "Solve the rational equation\r<BR>\n" );
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document.write( "x^3 / 16 = x^6 / 2\r<BR>\n" );
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document.write( "I keep getting an answer that is not listed as a possible answer.<BR>\n" );
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document.write( "I am using the symbol \"/\" as the fraction symbol not the division symbol.\r<BR>\n" );
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document.write( "And thank you for your help.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #358988 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=358988\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the LCD of the fractions in the equation 4.5x / 2x+5 = 2x / x^2 <BR>\n" );
document.write( "I keep getting the answer (2x+5)(x) But it does not seem correct to me. <BR>\n" );
document.write( "On the RHS, 2x/x^2 = 2/x<BR>\n" );
document.write( "The LCD is x(2x+5)<BR>\n" );
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document.write( "Solve each equation if no real answer then select no real answer. <BR>\n" );
document.write( "x / x-5 = -2x/x<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+=+-2x%28x-5%29+=+-2x%5E2+%2B+10x ALIGN=MIDDLE  ALT=\"x%5E2+=+-2x%28x-5%29+=+-2x%5E2+%2B+10x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2+-+10x+=+0 ALIGN=MIDDLE  ALT=\"3x%5E2+-+10x+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 0<BR>\n" );
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document.write( "3x = 10<BR>\n" );
document.write( "x = 10/3<BR>\n" );
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document.write( "I keep getting x=10 in every way I try to solve the problem and it is not listed as one of the possible answers, I marked no real solution.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "For this problem I do not understand on how to attempt it. <BR>\n" );
document.write( "Find the focal length of the magnifying glass if you can see the butterfly clearly when your eye is 5.5 cm away from the glass and the glass is 25 cm away from the butterfly. The formula is 1/s + 1/t = 1/f. <BR>\n" );
document.write( "I do not understand on how to do it. <BR>\n" );
document.write( "What are s, t & f?<BR>\n" );
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document.write( "Simplify the rational equations. <BR>\n" );
document.write( "x+5 / 3x+15<BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B5%29%2F%283%28x%2B5%29%29 ALIGN=MIDDLE  ALT=\"%28x%2B5%29%2F%283%28x%2B5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "= 1/3<BR>\n" );
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document.write( "I think it is in the simplist form already but I know you can divide the 5 into the 15 but can't divide the 3x into 3 . <BR>\n" );
document.write( "x+5/4 divided by (x^2+5x) <BR>\n" );
document.write( "I got 1/4x but i do not think it is correct. <BR>\n" );
document.write( "--- <BR>\n" );
document.write( "Solve the rational equation <BR>\n" );
document.write( "x^3 / 16 = x^6 / 2<BR>\n" );
document.write( "Multiply by 16<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+=+8x%5E6 ALIGN=MIDDLE  ALT=\"x%5E3+=+8x%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%5E6+-+x%5E3+=+0 ALIGN=MIDDLE  ALT=\"8x%5E6+-+x%5E3+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%2A%288x%5E3+-+1%29+=+0 ALIGN=MIDDLE  ALT=\"x%5E3%2A%288x%5E3+-+1%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 0 (multiplicity 3)<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%5E3+-+1+=+0 ALIGN=MIDDLE  ALT=\"8x%5E3+-+1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x-1%29%2A%284x%5E2+%2B+2x+%2B+1%29 ALIGN=MIDDLE  ALT=\"%282x-1%29%2A%284x%5E2+%2B+2x+%2B+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 1/2<BR>\n" );
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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=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</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=4x%5E2%2B2x%2B1+=+0 ALIGN=MIDDLE  ALT=\"4x%5E2%2B2x%2B1+=+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=%282%29%5E2-4%2A4%2A1=-12 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%282%29%5E2-4%2A4%2A1=-12\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  The discriminant -12 is less than zero. That means that there are no solutions among real numbers.<BR><BR>\n" );
document.write( "  If you are a student of advanced school algebra and are aware about <u>imaginary numbers<u>, read on.<BR><BR>\n" );
document.write( "  <BR>\n" );
document.write( "      In the field of imaginary numbers, the square root of -12 is + or - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28+12%29+=+3.46410161513775 ALIGN=MIDDLE  ALT=\"sqrt%28+12%29+=+3.46410161513775\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <BR>\n" );
document.write( "  <BR>\n" );
document.write( "      The solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28-2%2B-i%2Asqrt%28+-12+%29%29%2F2%5C4+=++%28-2%2B-i%2A3.46410161513775%29%2F2%5C4+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >, or<BR>\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+4%2Ax%5E2%2B2%2Ax%2B1+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B2%2Ax%2B1+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "It's 6th order --> 6 solutions:<BR>\n" );
document.write( "0,0,0,1/2, and the 2 complex numbers.<BR>\n" );
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document.write( "I keep getting an answer that is not listed as a possible answer.<BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );