document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=277511>Question 277511</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The question is:\r<BR>\n" );
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document.write( "simplify 4 + x^-1<BR>\n" );
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document.write( "         64+ x^-3\r<BR>\n" );
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document.write( "I factored the terms and made the exponents positive.\r<BR>\n" );
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document.write( "4+x^1<BR>\n" );
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document.write( "(4+x)(4-x)(4-x)\r<BR>\n" );
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document.write( "x^3 minus x = x^2 which is the numerator of the answer.\r<BR>\n" );
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document.write( "(4+x) is cross cancelled leaving the denominator of the answer to be 16.\r<BR>\n" );
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document.write( "I think the answer is \r<BR>\n" );
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document.write( "X^2<BR>\n" );
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document.write( "16\r<BR>\n" );
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document.write( "Any help is welcome. Thank you.\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 #202029 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=202029\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> simplify 4 + x^-1<BR>\n" );
document.write( "________<BR>\n" );
document.write( "64+ x^-3 <BR>\n" );
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document.write( "I factored the terms and made the exponents positive. <BR>\n" );
document.write( "4+x^1<BR>\n" );
document.write( "______<BR>\n" );
document.write( "(4+x)(4-x)(4-x) <BR>\n" );
document.write( "x^3 minus x = x^2 which is the numerator of the answer. <BR>\n" );
document.write( "(4+x) is cross cancelled leaving the denominator of the answer to be 16. <BR>\n" );
document.write( "I think the answer is <BR>\n" );
document.write( "X^2<BR>\n" );
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document.write( "16 <BR>\n" );
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document.write( "x^-1 = 1/x<BR>\n" );
document.write( "x^-3 = 1/x^3<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64%2Bx%5E-3+=+4%5E3+-+%281%2Fx%29%5E3 ALIGN=MIDDLE  ALT=\"64%2Bx%5E-3+=+4%5E3+-+%281%2Fx%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284+%2B+%281%2Fx%29%29%2A%2816+-+%281%2Fx%29+%2B+%281%2Fx%29%5E2%29 ALIGN=MIDDLE  ALT=\"%284+%2B+%281%2Fx%29%29%2A%2816+-+%281%2Fx%29+%2B+%281%2Fx%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The numerator is the 1st term, so cancel those.<BR>\n" );
document.write( "--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%2816+-+%281%2Fx%29+%2B+%281%2Fx%29%5E2%29 ALIGN=MIDDLE  ALT=\"1%2F%2816+-+%281%2Fx%29+%2B+%281%2Fx%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%2816+-+x%5E-1+%2B+x%5E-2%29 ALIGN=MIDDLE  ALT=\"1%2F%2816+-+x%5E-1+%2B+x%5E-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "I factored the terms and made the exponents positive. *** Changing the exponents is not allowed.\r<BR>\n" );
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