document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=905083>Question 905083</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello,\r<BR>\n" );
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document.write( "Problem:<BR>\n" );
document.write( "Given the equation xy + 3y = 2x + 1, show that y is a function of x and determine the domain in interval notation.\r<BR>\n" );
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document.write( "Thank you in advance,<BR>\n" );
document.write( "Ryan\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 #549019 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=549019\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First solve for y\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy+%2B+3y+=+2x+%2B+1 ALIGN=MIDDLE  ALT=\"xy+%2B+3y+=+2x+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%28x+%2B+3%29+=+2x+%2B+1 ALIGN=MIDDLE  ALT=\"y%28x+%2B+3%29+=+2x+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%282x+%2B+1%29%2F%28x+%2B+3%29 ALIGN=MIDDLE  ALT=\"y+=+%282x+%2B+1%29%2F%28x+%2B+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The function is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%282x+%2B+1%29%2F%28x+%2B+3%29 ALIGN=MIDDLE  ALT=\"y+=+%282x+%2B+1%29%2F%28x+%2B+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which can also be written as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+%282x+%2B+1%29%2F%28x+%2B+3%29 ALIGN=MIDDLE  ALT=\"f%28x%29+=+%282x+%2B+1%29%2F%28x+%2B+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (since y = f(x))\r<BR>\n" );
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document.write( "You cannot divide by zero. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3 ALIGN=MIDDLE  ALT=\"x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the denominator, can't be equal to zero. Set it equal to zero and solve for x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3=0 ALIGN=MIDDLE  ALT=\"x%2B3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3 ALIGN=MIDDLE  ALT=\"x=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The value <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3 ALIGN=MIDDLE  ALT=\"x=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > causes the denominator to be zero. Therefore, we must kick it out of the domain. Any other real number is perfectly fine since it doesn't cause a division by zero error.\r<BR>\n" );
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document.write( "Domain: Set of all real numbers x such that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E-3 ALIGN=MIDDLE  ALT=\"x%3C%3E-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Domain in interval notation: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (-\infty,-3)\cup(-3,\infty)\"> </SPAN>\n" );
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