document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=201183>Question 201183</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1)The length of a rectangle is 1 meter less than four times the width. If the area of the rectangle is 60 square meters, find the dimensions. Width____ft, Lenth_____ft.\r<BR>\n" );
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document.write( "2  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2F%28x%5E2+-+1%29%29-%28%28x%2B2%29%2F%28x%5E2+%2B+3x+-+4%29%29 ALIGN=MIDDLE  ALT=\"%282x%2F%28x%5E2+-+1%29%29-%28%28x%2B2%29%2F%28x%5E2+%2B+3x+-+4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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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 #151389 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=151389\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "1)  Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> represent the width.  Then the length is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 4x - 1\">.\r<BR>\n" );
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document.write( "The area is the product of the length and the width, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x(4x - 1) = 60\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 4x^2 - x - 60 = 0\">\r<BR>\n" );
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document.write( "Solve the quadratic (it factors).  Exclude the negative root because you are looking for a positive measure of length.  The positive root will be your width.\r<BR>\n" );
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document.write( "2) <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{2x}{x^2 - 1}-\frac{x+2}{x^2 + 3x - 4}\">\r<BR>\n" );
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document.write( "Factor both denominators:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{2x}{(x + 1)(x - 1)}-\frac{x+2}{(x + 4)(x - 1)}\">\r<BR>\n" );
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document.write( "The LCD is then:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (x + 1)(x - 1)(x + 4)\">\r<BR>\n" );
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document.write( "Apply the LCD:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{2x(x + 4)}{(x + 1)(x - 1)(x + 4)}-\frac{(x + 2)(x + 1)}{(x + 1)(x - 1)(x + 4)}\">\r<BR>\n" );
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document.write( "Distribute and apply FOIL to the numerators:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{2x^2 + 8x}{(x + 1)(x - 1)(x + 4)}-\frac{x^2 + 3x + 2}{(x + 1)(x - 1)(x + 4)}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{2x^2 + 8x}{(x + 1)(x - 1)(x + 4)}+\frac{-(x^2 + 3x + 2)}{(x + 1)(x - 1)(x + 4)}\">\r<BR>\n" );
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document.write( "Add the numerators and collect like terms:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{x^2 + 5x - 2}{(x + 1)(x - 1)(x + 4)}\">\r<BR>\n" );
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document.write( "Since the numerator does not have rational factors, there are no common factors with the denominator, so expand the denominator and you are done:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{x^2 + 5x - 2}{(x^2 - 1)(x + 4)}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{x^2 + 5x - 2}{x^3 + 4x^2 - x - 4}\">\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" );
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