How do you solve \(\frac{6}{b-1} = \frac{9}{7}\)?
Answer (3)
b − 1 6 = 7 9 b − 1 = 0 b = 1 b ∈ R ∖ { 1 } 9 ( b − 1 ) = 6 ∗ 7 9 b − 9 = 42 9 b = 42 + 9 9 b = 51 / : 9 b = 9 51 b = 5 9 6 b = 5 3 2
(6/b)-1 = 9/7 6/b = (9/7)+1 6 = [(9/7)+1]*b
6/[(9/7)+1] = b
b = 21/9
To solve b − 1 6 = 7 9 , we cross-multiply to get 42 = 9 ( b − 1 ) , then isolate b to find b = 5 3 2 . Always check to ensure the solution does not make any denominator zero. This solution is valid since b = 1 .
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