document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=486078>Question 486078</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the following quotient:\r<BR>\n" );
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document.write( "3x^2-25y^2/3x+5y\r<BR>\n" );
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document.write( "I did this and got x-5y, I then checked it on a math site with calculator and<BR>\n" );
document.write( "it said the answer was x with a remainder of 0. how am I wrong?????\r<BR>\n" );
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document.write( "because I did another one x^2-36/x+6 and got x-6 which was correct.<BR>\n" );
document.write( "doesn't the same apply to the first one.   Thanks for any input. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #332345 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=332345\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Well, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ -\ 5y\"> is the quotient although it is an incomplete answer because there is a remainder involved. <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> remainder 0 is completely out to lunch.  (<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (x)(3x\ -\ 5y)\ =\ 3x^2\ -\ 5xy\ \neq\ 3x^2\ -\ 25y^2\">)\r<BR>\n" );
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document.write( "The reason <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{x^2\ -\ 36}{x\ +\ 6}\"> comes out so tidily is NOT because \"x goes in to x-squared x times and 6 goes into 36 six times\" but rather because of the factorization of the numerator.  Note that the numerator is the difference of two squares, so\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{x^2\ -\ 36}{x\ +\ 6}\ =\ \frac{(x\ +\ 6)(x\ -\ 6)}{x\ +\ 6}\ =\ x\ -\ 6,\ x\ \neq\ -6\">\r<BR>\n" );
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document.write( "Considering the number 3 to be the square of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \sqrt{3}\">, you can factor the numerator of your problem as the difference of two squares:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 3x^2\ -\ 25y^2\ =\ \left(\left(\sqrt{3}\right)x\ -\ 5y\right)\left(\left(\sqrt{3}\right)x\ +\ 5y\right)\">\r<BR>\n" );
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document.write( "but neither of these factors is evenly divisible by your given denominator, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 3x\ +\ 5y\">\r<BR>\n" );
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document.write( "The only thing left to us is to do multi-variable polynomial long division.  A process that is very difficult and time consuming to render on this system.  Perhaps you can get an idea from:\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF=\"http://www.mathsisfun.com/algebra/polynomials-division-long.html<BR>\n" );
document.write( "\">MathIsFun Polynomial Long Division</a>  (scroll all the way down to the bottom of the page for the multi-variable process)\r<BR>\n" );
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document.write( "Properly performed you should obtain the quotient that you mentioned, but also with a remainder of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 10xy\">\r<BR>\n" );
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document.write( "In summary:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{3x^2\ -\ 25y^2}{3x\ +\ 5y}\ =\ x\ -\ 5y\ +\ \frac{10xy}{3x\ +\ 5y}\"> \r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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