## Algebra: A Combined Approach (4th Edition)

This rational expression is undefined for $x=-\dfrac{3}{2}$ and $x=\dfrac{5}{2}$
$\dfrac{5x+9}{4x^{2}-4x-15}$ 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 $x=\dfrac{5}{2}$