b^2/12/(b/4/5/b)
To simplify the expression b^2/12/(b/4/5/b), let's break it down step by step:
Step 1: Simplify the denominator
Since the denominator contains divisions, we need to simplify it from left to right.
b/4/5/b can be rewritten as (b/4) * (1/5) * (1/b).
The b in the numerator and denominator cancels out, and the resulting denominator is (4 * 5) = 20.
Now the expression becomes b^2/12/20.
Step 2: Simplify the division
To divide by a fraction, we can multiply by its reciprocal. In this case, we need to divide b^2/12 by 20, which is equivalent to multiplying by 1/20.
The expression can be rewritten as: b^2/12 * (1/20).
Step 3: Simplify further
Now, we just need to simplify the multiplication of fractions.
To multiply two fractions, we multiply the numerators and multiply the denominators.
b^2 * 1
------------ (notice that 12 and 20 share a common factor of 4)
12 * 20
Simplifying gives us:
b^2
------
4 * 5
This can be further simplified by simplifying the numerator and denominator separately.
The numerator, b^2, does not have any like terms to simplify.
The denominator, 4 * 5, equals 20.
So, the final simplified expression is: b^2/20.
In summary, the expression b^2/12/(b/4/5/b) simplifies to b^2/20 by following the steps of breaking down the denominators, simplifying divisions, and then simplifying the multiplication of fractions.