As practice, “simplify” all of these expressions: write them as nicely as possible, consolidating operations on fractions into single fractions. You can check your answer by testing the initial expression and your result at some simple values of the variables to ensure they’re equal.
\(\displaystyle \frac{a}{3}+\frac{b}{5} \)
\(\displaystyle \frac{12}{r}+\frac{2}{9} \)
\(\displaystyle \frac{2}{c}+\frac{7}{y} \)
\(\displaystyle \frac{3}{x}+\frac{r}{8} \)
\(\displaystyle \frac{3}{t}-z \)
\(\displaystyle \frac{b}{2a}+\frac{7c}{d} \)
\(\displaystyle \frac{5x}{2}+\frac{7c}{d} \)
\(\displaystyle \frac{5x}{x+1}+\frac{19}{x} \)
\(\displaystyle \frac{x+1}{26x}+\frac{b}{13} \)
\(\displaystyle \frac{x+1}{y-1}+\frac{y+1}{x+1} \)
\(\displaystyle \frac{1+\tfrac{1}{x}}{\tfrac{1}{y}+1} \)