Answer
This rational expression is undefined for $x=-\dfrac{3}{2}$ and $x=\dfrac{5}{2}$
Work Step by Step
$\dfrac{5x+9}{4x^{2}-4x-15}$
This rational expression is undefined for the values of $x$ that make the denominator equal to $0$. Knowing this fact, we just need to solve the equation $4x^{2}-4x-15=0$ to find those values.
$4x^{2}-4x-15=0$
Solve this equation by factoring:
$(2x+3)(2x-5)=0$
Set each factor equal to $0$ and solve the two individual equations for $x$:
$2x+3=0$
$2x=-3$
$x=-\dfrac{3}{2}$
$2x-5=0$
$2x=5$
$x=\dfrac{5}{2}$
This rational expression is undefined for $x=-\dfrac{3}{2}$ and $x=\dfrac{5}{2}$
