Two Means - Unknown, Unequal Variance: Videos & Practice Problems

In a study comparing the amount of juice in two types of lemons, the sample sizes and standard deviations are:
Sample 1: $n_1=20,s_1=1.8\text{mL}$
Sample 2: $n_2=26,s_2=2.2\text{mL}$
When using the method of taking the smaller of $n_1-1$ and $n_2-1$, the degrees of freedom are $19$.
Find the number of degrees of freedom using the following formula.
$df=\frac{{(\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2})}^2}{\frac{{\left(\frac{s_1^2}{n_1}\right)}^2}{n_1-1}+\frac{{\left(\frac{s_2^2}{n_2}\right)}^2}{n_2-1}}$
Explain briefly how hypothesis tests and confidence intervals are affected by using the exact formula compared to the simple method.