document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=197213>Question 197213</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If f(x)= 3x^2 -27/ 18x + 30 and g(x) = x^2 -7x +12/ 3x^2 -7x -20 , find f(x) divided by g(x) for all values of x for which the expression is defined and express your answer in simplest form. Help is appreciated! Thank you!<BR>\n" );
document.write( "Solution:<BR>\n" );
document.write( "f(x)=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%5E2+-27%29%2F%2818x+%2B+30+%29 ALIGN=MIDDLE  ALT=\"%283x%5E2+-27%29%2F%2818x+%2B+30+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >------(1)<BR>\n" );
document.write( "g(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+-7x+%2B12%29%2F%283x%5E2+-7x+-20%29 ALIGN=MIDDLE  ALT=\"%28x%5E2+-7x+%2B12%29%2F%283x%5E2+-7x+-20%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ------(2)<BR>\n" );
document.write( "f(x)/g(x)==> f(x)*(1/g(x))<BR>\n" );
document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%283x%5E2-27%29%2F%2818x%2B30%29%29%2A%28%283x%5E2-7x-20%29%2F%28x%5E2-7x%2B12%29%29 ALIGN=MIDDLE  ALT=\"%28%283x%5E2-27%29%2F%2818x%2B30%29%29%2A%28%283x%5E2-7x-20%29%2F%28x%5E2-7x%2B12%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28x%5E2-9%29%2F6%283x%2B5%29%2A%28%283x%2B5%29%28x-4%29%29%2F%28%28x-4%29%28x-3%29%29 ALIGN=MIDDLE  ALT=\"3%28x%5E2-9%29%2F6%283x%2B5%29%2A%28%283x%2B5%29%28x-4%29%29%2F%28%28x-4%29%28x-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2B3%29%2Ahighlight%28%28x-3%29%29%2A%283x%2B5%29%2A%28x-4%29%29%2F%282%283x%2B5%29%2A%28x-4%29highlight%28%28x-3%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2B3%29%2Across%28%28x-3%29%29%2A%283x%2B5%29%2A%28x-4%29%29%2F%282%283x%2B5%29%2A%28x-4%29cross%28%28x-3%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2B3%29%2A%283x%2B5%29%2Ahighlight%28%28x-4%29%29%29%2F%282%283x%2B5%29%2Ahighlight%28%28x-4%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2B3%29%2A%283x%2B5%29%2Across%28%28x-4%29%29%29%2F%282%283x%2B5%29%2Across%28%28x-4%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2B3%29%2Ahighlight%28%283x%2B5%29%29%29%2F%282highlight%28%283x%2B5%29%29%29 ALIGN=MIDDLE  ALT=\"%28%28x%2B3%29%2Ahighlight%28%283x%2B5%29%29%29%2F%282highlight%28%283x%2B5%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2B3%29%2Across%28%283x%2B5%29%29%29%2F%282cross%28%283x%2B5%29%29%29 ALIGN=MIDDLE  ALT=\"%28%28x%2B3%29%2Across%28%283x%2B5%29%29%29%2F%282cross%28%283x%2B5%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the simplest form is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29%2F2 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #147857 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=147857\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If f(x)= 3x^2 -27/ 18x + 30 and g(x) = x^2 -7x +12/ 3x^2 -7x -20 , find f(x) divided by g(x) for all values of x for which the expression is defined and express your answer in simplest form. Help is appreciated! Thank you!<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "f(x) = [3(x-3)(x+3)]/[6(3x+5)]<BR>\n" );
document.write( "---------------------------------<BR>\n" );
document.write( "g(x) = [(x-3)(x-4)]/[3x^2 -12x + 5x - 20]<BR>\n" );
document.write( "= [(x-3)(x-4)]/[(x-4)(3x+5)]<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "Cancel the factors that are common to a numerator and a denominator to get:<BR>\n" );
document.write( "f(x)/g(x) = [(x+3)/2/[1/1]<BR>\n" );
document.write( "---<BR>\n" );
document.write( "f(x)/g(x) = [(x+3)/[2]<BR>\n" );
document.write( "========================================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );