Find all numbers for which the rational expression is undefined.
r^3-8r/r^2-25
If you have (r^2-25) in the denominator, then r=+- 5 is not allowed. It is not allowed to divide by zero.
To find the numbers for which a rational expression is undefined, you need to identify any values that make the denominator(s) equal to zero. In this case, the given rational expression is:
(r^3 - 8r) / (r^2 - 25)
So, we need to find the values of "r" that make the denominator (r^2 - 25) equal to zero. The denominator becomes zero when:
r^2 - 25 = 0
To solve this equation, we can factor it by recognizing that it is a difference of squares:
(r - 5)(r + 5) = 0
Now, we can set each factor equal to zero and solve for "r":
(r - 5) = 0 or (r + 5) = 0
Solving for both equations:
For (r - 5) = 0:
r = 5
For (r + 5) = 0:
r = -5
Therefore, the values at which the given rational expression is undefined are r = 5 and r = -5.