Divide using synthetic division $$ ( x+5 ) \div ( x-6 ) $$

The synthetic division table is:

$$ \begin{array}{c|rr}6&1&5\\& & \color{black}{6} \\ \hline &\color{blue}{1}&\color{orangered}{11} \end{array} $$

The solution is:

$$ \frac{ x+5 }{ x-6 } = \color{blue}{1} ~+~ \frac{ \color{red}{ 11 } }{ x-6 } $$

Step 1 : Write down the coefficients of the dividend into division table. Put the zero from $ x -6 = 0 $ ( $ x = \color{blue}{ 6 } $ ) at the left.

$$ \begin{array}{c|rr}\color{blue}{6}&1&5\\& & \\ \hline && \end{array} $$

Step 1 : Bring down the leading coefficient to the bottom row.

$$ \begin{array}{c|rr}6&\color{orangered}{ 1 }&5\\& & \\ \hline &\color{orangered}{1}& \end{array} $$

Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 6 } \cdot \color{blue}{ 1 } = \color{blue}{ 6 } $.

$$ \begin{array}{c|rr}\color{blue}{6}&1&5\\& & \color{blue}{6} \\ \hline &\color{blue}{1}& \end{array} $$

Step 3 : Add down last column: $ \color{orangered}{ 5 } + \color{orangered}{ 6 } = \color{orangered}{ 11 } $

$$ \begin{array}{c|rr}6&1&\color{orangered}{ 5 }\\& & \color{orangered}{6} \\ \hline &\color{blue}{1}&\color{orangered}{11} \end{array} $$

Bottom line represents the quotient $ \color{blue}{ 1 } $ with a remainder of $ \color{red}{ 11 } $.

Synthetic Division Calculator