Simplify $ \dfrac{j-7}{j-7} $ to $ 1$.

Factor both the denominator and the numerator, then cancel the common factor. $\color{blue}{j-7}$.

$$ \begin{aligned} \frac{j-7}{j-7} & =\frac{ 1 \cdot \color{blue}{ \left( j-7 \right) }}{ 1 \cdot \color{blue}{ \left( j-7 \right) }} = \\[1ex] &= \frac{1}{1} =1 \end{aligned} $$

Multiply $ \dfrac{5j+59}{j+7} $ by $ 1 $ to get $ \dfrac{ 5j+59 }{ j+7 } $.

Step 1: Write $ 1 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{5j+59}{j+7} \cdot 1 & \xlongequal{\text{Step 1}} \frac{5j+59}{j+7} \cdot \frac{1}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( 5j+59 \right) \cdot 1 }{ \left( j+7 \right) \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 5j+59 }{ j+7 } \end{aligned} $$