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Algebra/rational expressions

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Expert: - 1/20/2011


Question

photo371
i dont know how to type the equation so i uploded a picture

Answer
All that is in the picture is the equation.
If r is not 2 or -2, the expression can be evaluated.

To factor it at first, it is [(r-6)(r+1)]/[(r-2)(r+2)], so there are no terms that cancel.
Basically, it forms a graph with vertical assymptotes at 2 ad -2.  When x goes to infinity, the graph goes up to a horizontal assymptote of 1.  It goes down to 1 as x goees to -infinity.


To see how it looks, draw a line with a region to the left of -2, a region between -2 and -1,
a region between -1 and 2, a region between 2 and 6, and an region to the right of 6.

Write r-6, r+1, r-2, and r+2 on the left in a column.  In each of the intervals, put down the sign of the fuction.  For example, r-6 is negative in all of the line segments the are to the left of 6 and positive to the right.  Do the same for r+1, r-2, and r+2.

If there are an even number of negative terms in these four terms in a region,
the function will be positive.  If there is an odd number of negative terms in a region,
the graph will be negative.  At r=-2 and r=2, there are vertical assymptotes.
At r=-1 and r=6, the graph crosses the x axis.



By the way, the photo number, 371, is a very good number.  371 = 3^3 + 7^3 + 1^3,
for 3^3 = 3*3*3 = 27, 7^3 = 7*7*7 = 343, and 1^3 = 1*1*1 = 1.  That gives
27 + 343 + 1.  The other numbers with this property are 153, 370, and 407.

Also, looking at p-h-o-t-o, p is the 16th letter in the alphabet, h is the 8th letter,
o is the 15th letter, t is the 20th letter, and o is the 15th letter.
Now 16+8+15+20+15 = 74, and 5*74 = 370, which is one short of the number there and
another one of the special numbers mentioned.

Scott A Wilson

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