What are the discontinuities and zero of 5x / (x^2-25) ? show your work.

zero: x = 0

discontinuities: x = - 5, x = 5

Step-by-step explanation:

The zeros of the rational function will be found where the numerator is zero. That will happen when x=0.

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There will be discontinuities where the denominator is zero. The denominator is the difference of squares, so factors as ...

x^2 - 25 = (x - 5) (x + 5)

These factors will be zero when x=5 and x=-5.