document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=128546>Question 128546</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1-3x<BR>\n" );
document.write( "______<BR>\n" );
document.write( "3x^2+14x-5\r<BR>\n" );
document.write( "\n" );
document.write( "can you show me how to simplify </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #94056 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=94056\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given to simplify:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281-3x%29%2F%283x%5E2%2B14x-5%29 ALIGN=MIDDLE  ALT=\"%281-3x%29%2F%283x%5E2%2B14x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Since these are \"setup\" problems that are designed to teach a point, you can make a guess<BR>\n" );
document.write( "that the numerator and the denominator have a common term that cancels out.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Let's re-write the numerator that it is arranged in descending powers of x ... that is<BR>\n" );
document.write( "so the x term appears first followed by the constant. When we do that the problem becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3x%2B1%29%2F%283x%5E2%2B14x-5%29 ALIGN=MIDDLE  ALT=\"%28-3x%2B1%29%2F%283x%5E2%2B14x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Then in the numerator, factor out <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > so that we make the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x ALIGN=MIDDLE  ALT=\"3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > term positive. This makes the<BR>\n" );
document.write( "expression become:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%29%283x-1%29%2F%283x%5E2%2B14x-5%29 ALIGN=MIDDLE  ALT=\"%28-1%29%283x-1%29%2F%283x%5E2%2B14x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now let's see if we can factor the denominator. And let's guess that one of the factors<BR>\n" );
document.write( "might be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-1%29 ALIGN=MIDDLE  ALT=\"3x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This being the case we might begin the factoring with:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x+-1%29%2A%28Ax+%2B+B%29 ALIGN=MIDDLE  ALT=\"%283x+-1%29%2A%28Ax+%2B+B%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "We know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x ALIGN=MIDDLE  ALT=\"3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > times <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ax ALIGN=MIDDLE  ALT=\"Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" > has to equal the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2 ALIGN=MIDDLE  ALT=\"3x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the given denominator. Therefore,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" > will have to equal <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > so that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2A1x+=+3x%5E2 ALIGN=MIDDLE  ALT=\"3x%2A1x+=+3x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So go to our factored form of the denominator<BR>\n" );
document.write( "and substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" > to make the factored form:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x-1%29%2A%281x+%2B+B%29 ALIGN=MIDDLE  ALT=\"%283x-1%29%2A%281x+%2B+B%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Note that when we do the next step we just write the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x ALIGN=MIDDLE  ALT=\"1x\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Next from this factored form we can see that if we multiply the constant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > by<BR>\n" );
document.write( "B, it has to result in the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5 ALIGN=MIDDLE  ALT=\"-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the original denominator of the problem. So we can <BR>\n" );
document.write( "say that:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%29%2AB+=+-5 ALIGN=MIDDLE  ALT=\"%28-1%29%2AB+=+-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "and we can solve this for B by multiplying both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B+=+5 ALIGN=MIDDLE  ALT=\"B+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Substitute this value for B in the factored form of our denominator and you have that the<BR>\n" );
document.write( "factored form is:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x-1%29%2A%28x+%2B+5%29 ALIGN=MIDDLE  ALT=\"%283x-1%29%2A%28x+%2B+5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "You can check this out by doing the multiplication just to be sure that the product is<BR>\n" );
document.write( "equal to the original denominator.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Substitute this into the problem where we had rearranged the numerator and we now have:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%29%283x-1%29%2F%28%283x-1%29%2A%28x%2B5%29%29 ALIGN=MIDDLE  ALT=\"%28-1%29%283x-1%29%2F%28%283x-1%29%2A%28x%2B5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Cancel the common factor in the numerator with the same factor in the denominator:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%29%2A%28cross%283x-1%29%29%2F%28%28cross%283x-1%29%29%2A%28x%2B5%29%29 ALIGN=MIDDLE  ALT=\"%28-1%29%2A%28cross%283x-1%29%29%2F%28%28cross%283x-1%29%29%2A%28x%2B5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "And you are left with the simplified form:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F%28x%2B5%29 ALIGN=MIDDLE  ALT=\"-1%2F%28x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "and that's your answer. <BR>\n" );
document.write( ".<BR>\n" );
document.write( "Hope this explanation helps you to understand the problem.<BR>\n" );
document.write( ". </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );