6b-1=97

Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

6⋅7=(b-1)⋅9

Rewrite the equation as (b-1)⋅9=6⋅7.

(b-1)⋅9=6⋅7

Multiply 6 by 7.

(b-1)⋅9=42

Divide each term by 9 and simplify.

Divide each term in (b-1)⋅9=42 by 9.

(b-1)⋅99=429

Cancel the common factor of 9.

Cancel the common factor.

(b-1)⋅99=429

Divide b-1 by 1.

b-1=429

b-1=429

Cancel the common factor of 42 and 9.

Factor 3 out of 42.

b-1=3(14)9

Cancel the common factors.

Factor 3 out of 9.

b-1=3⋅143⋅3

Cancel the common factor.

b-1=3⋅143⋅3

Rewrite the expression.

b-1=143

b-1=143

b-1=143

b-1=143

Move all terms not containing b to the right side of the equation.

Add 1 to both sides of the equation.

b=143+1

Write 1 as a fraction with a common denominator.

b=143+33

Combine the numerators over the common denominator.

b=14+33

Add 14 and 3.

b=173

b=173

b=173

The result can be shown in multiple forms.

Exact Form:

b=173

Decimal Form:

b=5.6‾

Mixed Number Form:

b=523

Solve for b 6/(b-1)=9/7