Answer
$a.\displaystyle \quad\frac{80}{t^{2}+4t+1}$
$b.\quad 13.3^{\circ}F, \ \ 6.2^{\circ}F$
Work Step by Step
$a.$
To add/subtract rational expressions with the same denominator,
add/subtract numerators and place the sum/difference over the common denominator.
$\displaystyle \frac{t+30}{t^{2}+4t+1}-\frac{t-50}{t^{2}+4t+1}=\frac{t+30-(t-50)}{t^{2}+4t+1}$
$=\displaystyle \frac{t+30-t+50}{t^{2}+4t+1}$
$=\displaystyle \frac{80}{t^{2}+4t+1}$
$b.$
After t=1 hour, $\displaystyle \frac{80}{1+4+1}=\frac{80}{6}\approx 13.3^{\circ}F$
After t=2 hours, $\displaystyle \frac{80}{4+8+1}=\frac{80}{13}\approx 6.2^{\circ}F$
