SOLUTION: i need help with the steps to complete this.find all numbers for which the rational expression is undefined.(r^3-8r)/(r^2-64)

Question 446094: i need help with the steps to complete this.find all numbers for which the rational expression is undefined.(r^3-8r)/(r^2-64)
Found 2 solutions by stanbon, Leaf W.:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
i need help with the steps to complete this.find all numbers for which the rational expression is undefined.
(r^3-8r)/(r^2-64)
Factor:
= [r(r^2-8)]/[(r-8)(r+8)]
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= [r(r-2sqrt(2))(r+2sqrt(2)]/[(r-8)(r+8)]
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undefined whent the denominator is zero.
undefined for r = 8 and for r = -8
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Cheers,
Stan H.
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Answer by Leaf W.(135) (Show Source): You can put this solution on YOUR website!
A solution or number is undefined when a positive or negative real number is divided by zero. Therefore, all you need to look at is the denominator, , and find the values that would make it equal to zero.
***First, factor it (NOTE: you could also use the quadratic formula, but I think factoring is easier in this case). Since it is a difference of squares, it factors to (r+8)(r-8).
***Second, Find the values that would make (r+8)(r-8) equal zero. If either of the two expressions (r+8 or r-8) were to equal zero, the entire (r+8)(r-8) would equal zero because no matter what the other expression was, anything multiplied by zero is zero. To find the values of r that would make either of the two expressions equal to zero, set them up as r+8=0 and r-8=0 and solve for r to get r=-8 and r=8. Therefore, the expression would be undefined if r were to equal -8 or 8.
***Just to show you how this works, let's plug these values into the expression, looking for a denominator of 0 to signal an undefined expression.
==> r=-8

<-- Division by zero--undefined!
==> r=8

<-- Division by zero--undefined!
***Therefore, the set of r = {-8, 8} would result in an undefined expression.
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