Question

Please help!!!!!

removable discontinuity of
1. d(x)=(x^2-12x+20)/(3x)
2. z(x)=(x^2-7x-8)/(x^3+64)
3. f(x)=(2x^3-3x+1)/(x^3-5x+7)
4. y=(x^2+4x-5)/(x^2+8x+15)

Answer 1

Several of these rational functions do not have a removable discontinuity.

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In a rational function, a removable discontinuity is generally found where numerator and denominator factors cancel. None of the denominator factors here is matched by a numerator factor, so the discontinuity that a denominator zero creates cannot be removed by defining the function at that point.

The function y = ( )/( ) has two discontinuities: one at x=-3, another at x=-5. The (x+5) factor in the denominator is matched by an (x+5) factor in the numerator, so there is a removable discontinuity at x=-5. That discontinuity can be removed by defining y=3 at that point.

Only 4. y = ... has a removable discontinuity.