Dividing by 3/8 and then multiplying by 5/6 is equivalent to dividing by what number ?

Question

Multiplying my age by 6 then subtracting 6 produces the same result as subtracting 7 from my age then multiplying by 7. How old am I?

Answer 1

9/20
Dividing by 3/8 means multiplying the number with 8/3.
Number x 8/3 x 5/6 = Number x 40/18 = Number x 20/9
= Number divided by 9/20