document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=391155>Question 391155</A>: <I><SPAN STYLE=\"word-break: break-all;\"> can you please help me work out this problem. i need to find the range of this function: {{3+x^2/ 4-x^2}}. i tried writing the problem as two binomials on top and two binomials on the bottom and solve for x but i am not sure if that is what i am suppose to do. so can you please help me solve this problem.<BR>\n" );
document.write( "Thank you so much for your time.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #277492 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=277492\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I will assume that your function is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%283%2Bx%5E2%29%2F%284-x%5E2%29 ALIGN=MIDDLE  ALT=\"y+=+%283%2Bx%5E2%29%2F%284-x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "To find the range solve for x in terms of y and then state conditions on y that may arise.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%283%2Bx%5E2%29%2F%284-x%5E2%29 ALIGN=MIDDLE  ALT=\"y+=+%283%2Bx%5E2%29%2F%284-x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y+-+yx%5E2+=+3+%2B+x%5E2 ALIGN=MIDDLE  ALT=\"4y+-+yx%5E2+=+3+%2B+x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+%281%2By%29x%5E2+-+4y+%2B+3 ALIGN=MIDDLE  ALT=\"0+=+%281%2By%29x%5E2+-+4y+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%280+%2B-+sqrt%28-4%2A%281%2By%29%2A%283-4y%29+%29%29%2F%282%2A%281%2By%29%29+=+%28+0%2B-+sqrt%28+%284y+-+3%29%281%2By%29%29%29%2F%281%2By%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >, using the quadratic formula.<BR>\n" );
document.write( "Since the values of x must be real, the conditions we should impose on y are \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%281%2By%29%2A%283-4y%29%3E=+0 ALIGN=MIDDLE  ALT=\"+%281%2By%29%2A%283-4y%29%3E=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and y is not equal to -1.<BR>\n" );
document.write( "The solution set to this inequality is the union of intervals (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-infinity ALIGN=MIDDLE  ALT=\"-infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >, -1)U[3/4, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=infinity ALIGN=MIDDLE  ALT=\"infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >).  This is the RANGE of the function.<BR>\n" );
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