$\begin{array} { l }\frac{ 6 }{ b-1 }=\frac{ 9 }{ 7 },& b≠1\end{array}$
Simplify the equation using cross-multiplication$42=9\left( b-1 \right)$
Distribute $9$ through the parentheses$42=9b-9$
Move the variable to the left-hand side and change its sign$42-9b=-9$
Move the constant to the right-hand side and change its sign$-9b=-9-42$
Calculate the difference$-9b=-51$
Divide both sides of the equation by $-9$$\begin{array} { l }b=\frac{ 17 }{ 3 },& b≠1\end{array}$
Check if the solution is in the defined range$\begin{align*}&b=\frac{ 17 }{ 3 } \\&\begin{array} { l }b=5 \frac{ 2 }{ 3 },& b=5.\overset{ \cdot }{ 6 } \end{array}\end{align*}$