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:
 $\frac{5x^2 + 26x + 24}{3x^2 + 10x - 8}$
 What we must do for this case, is to factor the numerator and the denominator.
 We have then:
 $\frac{(5x+6)(x+4)}{(3x-2)(x+4)}$
 Then, canceling similar terms we have:
 $\frac{(5x+6)}{(3x-2)}$
 Then, the function is not defined for the values that make the denominator zero.
 We have then:
 $3x-2 = 0 3x = 2$
 $x = \frac{2}{3}$
 And on the other hand, a zero of the function is:
 $5x+6 = 0 5x = -6$
 $x = \frac{-6}{5}$
 Answer:
 a zero of the function is:
 $x = \frac{-6}{5}$
 the function is not defined for the value:
 $x = \frac{2}{3}$