\[\begin{array}{rl} t_{ds}=t_{us}&\text{Set }t\text{'s equal to each other} \\ \dfrac{30}{r+2}=8-\dfrac{30}{r-2}&\text{Multiply by the LCD} \\ \color{blue}{(r+2)(r-2)}\color{black}{}\cdot\dfrac{30}{r+...\[\begin{array}{rl} t_{ds}=t_{us}&\text{Set }t\text{'s equal to each other} \\ \dfrac{30}{r+2}=8-\dfrac{30}{r-2}&\text{Multiply by the LCD} \\ \color{blue}{(r+2)(r-2)}\color{black}{}\cdot\dfrac{30}{r+2}=\color{blue}{(r+2)(r-2)}\color{black}{}\cdot 8-\color{blue}{(r+2)(r-2)}\color{black}{}\cdot\dfrac{30}{r-2}&\text{Clear denominators} \\ 30(r-2)=8(r+2)(r-2)-30(r+2)&\text{Distribute} \\ 30r-60=8r^2-32-30r-60&\text{Combine like terms} \\ 30r-60=8r^2-30r-92&\text{Notice the }8r^2\text{ term; solve …
