(6/b)-1 = 9/7 6/b = (9/7)+1 6 = [(9/7)+1]*b 6/[(9/7)+1] = b b = 21/9

[latex]\frac{6}{b-1} =\frac{9}{7} \\ \\b-1\neq 0\\ \\b\neq 1\\ \\b \in R\setminus \left \{ 1 \right \}\\ \\9(b-1)=6*7\\ \\ 9b-9=42\\ \\9b=42+9\\ \\9b=51 \ \ /:9\\ \\b=\frac{51}{9}\\ \\b=5\frac{6}{9}\\ \\b=5\frac{2}{3}[/latex]