## Intermediate Algebra: Connecting Concepts through Application

$\text{all real numbers except }$ $t=-\dfrac{5}{4}$
$\bf{\text{Solution Outline:}}$ The domain of the given rational function, $p(t)=\dfrac{3t-7}{4t+5} ,$ are the values of $t$ which will NOT make the denominator equal to $0.$ $\bf{\text{Solution Details:}}$ Solving for the values of $t$ that will make the denominator equal to $0$ results to \begin{array}{l}\require{cancel} 4t+5=0 \\\\ 4t=-5 \\\\ t=-\dfrac{5}{4} .\end{array} Hence, the domain is the set of $\text{all real numbers except }$ $t=-\dfrac{5}{4} .$