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To solve the equation 

\[
\frac{6}{b - 1} = \frac{9}{7},
\]

we can use cross-multiplication to eliminate the fractions. This gives:

\[
6 \cdot 7 = 9 \cdot (b - 1).
\]

Expanding and simplifying this yields:

\[
42 = 9(b - 1).
\]

Distribute the 9:

\[
42 = 9b - 9.
\]

Add 9 to both sides:

\[
51 = 9b.
\]

Finally, divide by 9:

\[
b = \frac{51}{9} = 5.67.
\]

Thus, the solution is:

\[
b \approx 5.67.
\]

Would you like a more detailed explanation, or do you have any questions?

Here are 5 related questions to expand your understanding:

1. How can you verify the solution for \( b \) in this type of equation?
2. What is cross-multiplication, and why does it work for solving equations with fractions?
3. What would happen if the denominator in the equation was zero?
4. How do you solve equations like this if they involve negative values?
5. How does solving an equation change if it involves more than one variable?

**Tip:** Always double-check that the values you find do not make any denominator zero, as division by zero is undefined.

Learn how to solve the rational equation 6 / (b - 1) = 9 / 7 with a step-by-step guide. This example demonstrates cross-multiplication and algebraic manipulation to find the solution for b, suitable for students in Grades 8-10.

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