ADDING AND SUBTRACTING SIMPLE FRACTIONS WITH VARIABLES
EXAMPLES:
Question: Combine into a single fraction: $\displaystyle\,\frac{2x}{5} + \frac{1}{3}$
Solution:   Notice that the least common denominator is $\,15\,$.

$\displaystyle \,\frac{2x}{5} + \frac{1}{3} \ \ =\ \ \frac{2x}{5}\cdot\frac{3}{3} + \frac{1}{3}\cdot\frac{5}{5} \ \ =\ \ \frac{6x}{15} + \frac{5}{15} \ \ =\ \ \frac{6x+5}{15}$
Question: Combine into a single fraction: $\displaystyle\,\frac{2}{9t} - \frac{1}{6}$
Solution:   Notice that the least common denominator is $\,18t\,$.

$\displaystyle \,\frac{2}{9t} - \frac{1}{6} \ \ =\ \ \frac{2}{9t}\cdot\frac{2}{2} - \frac{1}{6}\cdot\frac{3t}{3t} \ \ =\ \ \frac{4}{18t} - \frac{3t}{18t} \ \ =\ \ \frac{4-3t}{18t}$
Master the ideas from this section