Question

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

Answer 1

zero: x = 0

discontinuities: x = -5, x = 5

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.