document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=191061>Question 191061</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/1602773033/algebrahomeworkh>saxon algebra2</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> solve.<BR>\n" );
document.write( "3x/x^2-1=5/x<BR>\n" );
document.write( "I worked it out to:<BR>\n" );
document.write( "2(x-5)(x+1)<BR>\n" );
document.write( "Is this correct? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #143450 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=143450\">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( "Well, I will give you high marks for creativity.  But your answer isn't even close.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  \frac{3x}{x^2 - 1} = \frac{5}{x}\">\r<BR>\n" );
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document.write( "The two denominators have no factors in common, so the LCD is simply the product of the two, or <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x(x^2 - 1)\">.  Multiplying that out would only confuse the issue, so let's leave it the way it is.  Applying the LCD:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{3x}{(x^2 - 1)}\left(\frac{x}{x}\right) = \frac{5}{x}\left(\frac{x^2-1}{x^2-1}\right) \ \ \Rightarrow\ \  \frac{3x^2}{x(x^2 - 1)} = \frac{5(x^2-1)}{x(x^2 -1)} \">\r<BR>\n" );
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document.write( "Now, use the distributive property on the numerator on the right:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  \frac{3x^2}{x(x^2 - 1)} = \frac{5x^2-5}{x(x^2 -1)}\">\r<BR>\n" );
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document.write( "Now we have two fractions equal to each other and they have equal denominators.  Therefore the numerators must be equal as well.  So:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 3x^2 = 5x^2 - 5\">\r<BR>\n" );
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document.write( "Add <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE -5x^2\"> to both sides:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ -2x^2 = -5\">\r<BR>\n" );
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document.write( "Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE -{1 \over 2}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2 = \frac{5}{2}\">\r<BR>\n" );
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document.write( "Take the square root:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x = \pm sqrt{\frac{5}{2}} = \pm \frac{sqrt{5}}{sqrt{2}}\">\r<BR>\n" );
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document.write( "But we still need to rationalize the denominator so multiply by 1 in the form of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{sqrt{2}}{sqrt{2}}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x = \pm \left(\frac{sqrt{5}}{sqrt{2}}\right) \left(\frac{sqrt{2}}{sqrt{2}}\right) = \pm \frac{sqrt{10}}{2}\">\r<BR>\n" );
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document.write( "You should check both answers to make certain that we didn't create an extraneous root in the action of squaring the variable during the solving process.\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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