document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=201758>Question 201758</A>: <I><SPAN STYLE=\"word-break: break-all;\"> perform indicated operation, simplifying if possible.<BR>\n" );
document.write( "x^2+3x-4/x^2-x-20 * 5x-25/5x^2-x please show step by step. also what is the difference between X^2+3x-4 and X^2-3x-4 how do you factor them I came up with (x+1)(x-4) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #152018 by </B><A HREF=/tutors/aboutme.mpl?userid=PRMath><B>PRMath(133)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=PRMath><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=152018\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> perform indicated operation, simplifying if possible.<BR>\n" );
document.write( "x^2+3x-4/x^2-x-20 * 5x-25/5x^2-x please show step by step. also what is the difference between X^2+3x-4 and X^2-3x-4 how do you factor them I came up with (x+1)(x-4)\r<BR>\n" );
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document.write( "Ok, first think back to grade school math for a second, because these concepts connect, k?  Remember that 4/4 equals 1, right?  That's one concept to keep in your mind.\r<BR>\n" );
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document.write( "Another concept is that you can cancel out FACTORS (multiplication) in a fraction.  For example:  4x/4 means that you can look at 4/4 and realize it equals 1 and then that just leaves the \"x\".  \r<BR>\n" );
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document.write( "Now that you have those thoughts in your head, let's look at your problem.\r<BR>\n" );
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document.write( "It is this:\r<BR>\n" );
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document.write( "x^2+3x-4/x^2-x-20 * 5x-25/5x^2-x \r<BR>\n" );
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document.write( "So I would first factor everything I could factor.  Let's start with:\r<BR>\n" );
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document.write( "x^2+3x-4.   You have to think, what can you use that will MULTIPLY to get \"-4\" yet at the same time, will ADD up to equal \"+3\".\r<BR>\n" );
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document.write( "So, let's factor in this way:   (x + 4)(x - 1)  \r<BR>\n" );
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document.write( "Remember FOIL?  Check to see if we factored correctly.\r<BR>\n" );
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document.write( "Let's now factor:  x^2-x-20 \r<BR>\n" );
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document.write( "Sooooo what can you do that will MULTIPLY to get \"-20\" yet at the same time, will ADD up to be \"-1\"?  \r<BR>\n" );
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document.write( "We can factor the equation this way:    (x - 5)(x + 4)\r<BR>\n" );
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document.write( "We are not done yet.  Now we have to factor:   5x-25\r<BR>\n" );
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document.write( "Do you see a number there that is common to both the \"5\" and the \"25\"???\r<BR>\n" );
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document.write( "How about the number \"5\"?\r<BR>\n" );
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document.write( "SOooo let's factor this way:    5(x - 5)\r<BR>\n" );
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document.write( "We are STILL not done.  Now we have to factor:  5x^2-x \r<BR>\n" );
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document.write( "What is common to the 5x^2 and the \"X\"?????  How about \"x\"??\r<BR>\n" );
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document.write( "So, let's factor this way:   x(5x - 1)\r<BR>\n" );
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document.write( "Wow, we just did a lot of factoring.  Now will will put that info all together to see what we can cancel out, k?\r<BR>\n" );
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document.write( "Here we go:\r<BR>\n" );
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document.write( "(x + 4)(x - 1)  5(x - 5)<BR>\n" );
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document.write( "(x - 5)(x + 4)  x(5x - 1)\r<BR>\n" );
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document.write( "The above is the SAME problem you wrote, but everything has been factored out.  Now we can do some canceling.  I'm not sure how to show this to you. I really want to highlight the cancellations or do a strike over.  Hmmmm.  \r<BR>\n" );
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document.write( "(x + 4)(x - 1)  5(x - 5)<BR>\n" );
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document.write( "(x - 5)(x + 4)  x(5x - 1)\r<BR>\n" );
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document.write( "I think the only thing I can do is tell you in this way:\r<BR>\n" );
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document.write( "(x+4)in the numerator cancels out (x+4) in the denominator.<BR>\n" );
document.write( "(x-5) in the numerator cancels out (x-5) in the denominator.\r<BR>\n" );
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document.write( "Now you are left with:\r<BR>\n" );
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document.write( "(x - 1)5<BR>\n" );
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document.write( "x(5x - 1)\r<BR>\n" );
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document.write( "You cannot cancel out the \"X\" variables, because in the numerator (x - 1) is not factorable.  \r<BR>\n" );
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document.write( "So your answer is(assuming I understood what you wrote as the question) is:\r<BR>\n" );
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document.write( "5(x - 1)<BR>\n" );
document.write( "_________<BR>\n" );
document.write( "x(5x - 1)\r<BR>\n" );
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document.write( "You also wanted to know:  what is the difference between <BR>\n" );
document.write( "X^2+3x-4 and X^2-3x-4.  How do you factor them? I came up with (x+1)(x-4)\r<BR>\n" );
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document.write( "Here's your first equation: X^2+3x-4\r<BR>\n" );
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document.write( "Think of this:  What can you MULTIPLY to get \"-4\" and yet ADD to get \"+3\"\r<BR>\n" );
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document.write( "It would factor like this:   (x +4)(x-1)\r<BR>\n" );
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document.write( "Here's your 2nd equation:  X^2-3x-4\r<BR>\n" );
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document.write( "Again, what can you MULTIPLY to get \"-4\" and yet ADD to get a \"-3\".  (In the previous problem, you wanted a POSITIVE 3 but this time you want a NEGATIVE 3).\r<BR>\n" );
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document.write( "This 2nd equation would factor like this:  (x -4)(x +1)\r<BR>\n" );
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document.write( "Good luck.  Hope this helps. :-) </SPAN>\n" );
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