Question

Find the zero(s) of the rational expression below. fraction numerator 5 x squared plus 26 x plus 24 over denominator 3 x squared plus 10 x minus 8 end fraction

Answer 1

For this case we have the following rational expression:

`(5x^2 + 26x + 24)/(3x^2 + 10x - 8)`
What we must do for this case, is to factor the numerator and the denominator.
We have then:

`((5x+6)(x+4))/((3x-2)(x+4))`
Then, canceling similar terms we have:

`((5x+6))/((3x-2))`
Then, the function is not defined for the values that make the denominator zero.
We have then:

`3x-2 = 0 3x = 2`

`x = (2)/(3)`
And on the other hand, a zero of the function is:

`5x+6 = 0 5x = -6`

`x = (-6)/(5)`
Answer:
a zero of the function is:

`x = (-6)/(5)`
the function is not defined for the value:

`x = (2)/(3)`