Question

What value is a discontinuity of x squared plus 2 x plus 3, all over x squared minus x minus 12 ?

Answer 1

`x=-3, x=4`

Explanation:

we have

`(x^(2)+2x+3)/(x^(2)-x-12)`

we know that

The denominator can not be zero

Find the roots of the quadratic equation of denominator

`x^(2)-x-12=0`

using a graphing tool to resolve the quadratic equation

see the attached figure

The solutions are

`x=-3, x=4`

so

`x^(2)-x-12=(x+3)(x-4)`

therefore

we have

`(x^(2)+2x+3)/((x+3)(x-4))`

The values
`x=-3, x=4` are discontinuity of the original function