document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1033983>Question 1033983</A>: <I><SPAN STYLE=\"word-break: break-all;\"> given x is not equal to 7/4 and x is not equal to -1 simplify this rational this rational expression. what is the missing value? <BR>\n" );
document.write( "16^2-49/4x^2-3x-7=(4x+7)(4x-7)/(4x-7)(x+1)=______/x+1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #648582 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=648582\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i believe you meant 16x^2 - 49 as the numerator.\r<BR>\n" );
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document.write( "your equation becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2816x%5E2-49%29%2F%284x%5E2-3x-7%29+=+%28%284x%2B7%29%2A%284x-7%29%29%2F%28%284x-7%29%2A%28x%2B1%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "the (4x-7) in the numerator and the denominator cancel out and you are left with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x%2B7%29%2F%28x%2B1%29 ALIGN=MIDDLE  ALT=\"%284x%2B7%29%2F%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "i graphed all 3 equations so you can see what they look like.\r<BR>\n" );
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document.write( "the equation i graphed are:\r<BR>\n" );
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document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2816x%5E2-49%29%2F%284x%5E2-3x-7%29 ALIGN=MIDDLE  ALT=\"%2816x%5E2-49%29%2F%284x%5E2-3x-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%284x%2B7%29%2A%284x-7%29%29%2F%28%284x-7%29%2A%28x%2B1%29%29 ALIGN=MIDDLE  ALT=\"%28%284x%2B7%29%2A%284x-7%29%29%2F%28%284x-7%29%2A%28x%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x%2B7%29%2F%28x%2B1%29 ALIGN=MIDDLE  ALT=\"%284x%2B7%29%2F%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "all 3 equation generate the same graph.\r<BR>\n" );
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document.write( "there is no difference between the first two equations.\r<BR>\n" );
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document.write( "they will generate a vertical asymptote at x = -1 and a hole at x = 7/4.\r<BR>\n" );
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document.write( "the third equation is different in that it will not generate a hole at x = 7/4.\r<BR>\n" );
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document.write( "this is because, once you cancel out the same factor from the numerator and denominator, the resulting equation doesn't generate a hole because you no longer have a denominator that becomes 0 at that point.\r<BR>\n" );
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document.write( "the graph of all 3 equations is shown below.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2016/051102.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "to determine which equation give you a hole at 7/4, simply replace x with 7/4 in all 3 equations.\r<BR>\n" );
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document.write( "the first 2 equations should give you an undefined answer, while the third equation should give you a defined answer for the value of y.\r<BR>\n" );
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document.write( "i analyzed all 3 equations by replacing x with 7/4 in my ti-84+ calculator.\r<BR>\n" );
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document.write( "the first equation yielded y = divide by 0 error.\r<BR>\n" );
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document.write( "the second equation yielded y = divide by 0 error.\r<BR>\n" );
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document.write( "the third equation yielded y = 5.09090909....., which is equivalent to 5 + 1/11.\r<BR>\n" );
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document.write( "the graph shows you that the graph \"appears\" to be continuous at x = 7/4, even though there is a hole there for the first 2 equations.   it just can't be seen by the naked eye and is only discovered through analysis of the equation at that point.\r<BR>\n" );
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document.write( "the ti-84+ calculator will graph it, and has the ability to check for the value of x at certain point by just selecting that value of x.\r<BR>\n" );
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document.write( "for the first 2 equations, the ti-84+ will show you that the y value is blank.<BR>\n" );
document.write( "this is because there is no value at that point because it is undefined.\r<BR>\n" );
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document.write( "for the third equation, the ti-84+ will show you the y-value at that point.\r<BR>\n" );
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document.write( "in order to find the hole manually, you need to set the denominator equal to 0 and solve for x.\r<BR>\n" );
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document.write( "you also need to factor both numerator and denominator so that the same factor in the numerator and denominator show up.\r<BR>\n" );
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document.write( "you can't see that there is a hole by looking at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2816x%5E2-49%29%2F%284x%5E2-3x-7%29 ALIGN=MIDDLE  ALT=\"%2816x%5E2-49%29%2F%284x%5E2-3x-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "you can see that there is a hole by looking at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%284x%2B7%29%2A%284x-7%29%29%2F%28%284x-7%29%2A%28x%2B1%29%29 ALIGN=MIDDLE  ALT=\"%28%284x%2B7%29%2A%284x-7%29%29%2F%28%284x-7%29%2A%28x%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the numerator and denominator have the same factor, indicating there will be hole there and not an asymptote.\r<BR>\n" );
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document.write( "there will be an asymptote at x = -1 because the same factor doesn't appear in the numerator. </SPAN>\n" );
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