document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=359121>Question 359121</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Re: Simplifying Rational Expressions and Functions<BR>\n" );
document.write( "I understand how to write a function in simplified form using factoring and removing the factor = to 1. However, can someone walk me through the steps on determining the restrictions on the domain? I can't figure out how the restrictions on the domain are determined.<BR>\n" );
document.write( "Write the function given by<BR>\n" );
document.write( "g(x)= x^2+3x-10 / 2x^2-3x-2<BR>\n" );
document.write( "in simplified form, and list all the restrictions on the domain.\r<BR>\n" );
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document.write( "Answer: g(x)= x+5/2x+1, x cannot = -1/2 and x cannot = 2\r<BR>\n" );
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document.write( "Please teach me how to determine the restrictions. Thank you. Jill </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #256283 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=256283\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Write the function given by<BR>\n" );
document.write( "g(x)= x^2+3x-10 / 2x^2-3x-2<BR>\n" );
document.write( "in simplified form, and list all the restrictions on the domain. <BR>\n" );
document.write( "Answer: g(x)= x+5/2x+1, x cannot = -1/2 and x cannot = 2 <BR>\n" );
document.write( "Please teach me how to determine the restrictions.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "1st: Factor numerator and denominator if you can.<BR>\n" );
document.write( "[(x+5)(x-2)]/[(2x+1)(x-2)]<BR>\n" );
document.write( "---<BR>\n" );
document.write( "2nd: The function has a hole at x = 2 because you have<BR>\n" );
document.write( "the factor (x-2) in the numerator and in the denominator.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "3rd: The function is undefined at x = -1/2 because the <BR>\n" );
document.write( "factor (2x+1) is zero if x = -1/2.<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "Comment: As you get further into algebra you will run<BR>\n" );
document.write( "into Domain restrictions for two additional reasons:<BR>\n" );
document.write( "a) Ex: y = sqrt(x+2)<BR>\n" );
document.write( "Since x+2 must not be negative, x must be >= -2.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "b) Ex: y = log(x+2)<BR>\n" );
document.write( "Since x+2 must be positive, x must be > -2.<BR>\n" );
document.write( "===============<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );