ANSWER
[tex]b = 5\frac{2}{3} [/tex]
EXPLANATION
The given equation is
[tex] \frac{6}{b - 1} = \frac{9}{7} [/tex]
where b≠1.
We cross multiply to get,
[tex]7 \times 6 = 9(b - 1)[/tex]
Expand and multiply out to get,
[tex]42 = 9b - 9[/tex]
Group similar terms,
[tex]42 + 9 = 9b[/tex]
[tex]9b = 51[/tex]
Divide both sides by 9
[tex]b = \frac{51}{9} [/tex]
Simplify:
[tex]b = \frac{17}{3} [/tex]
Or
[tex] b = 5\frac{2}{3} [/tex]
