Question

Determine the point of discontinuity if it exists v(x)=x^2-25/2x^2+13x+15

Answer 1

Answer:

x=-5 and x=-1.5

Step-by-step explanation:

The given function is

$v(x) = \frac{{x}^{2} - 25}{2 {x}^{2} + 13x + 15}$

The points of discontinuity occurs at where the denominator is zero.

$2 {x}^{2} + 13x + 15= 0$

We solve by factoring.

We first split the middle term:

$2 {x}^{2} + 3x + 10x + 15= 0$

We factor by grouping:

$x(2x + 3) + 5(2x + 3)= 0$

$(x + 5)(2x + 3) = 0$

The points of discontinuity occur at x=-5, and x=-1.5