divide and simplify
5y-5/21 divided by y-1/33y
oh well, I suppose if you knew the how and why of parentheses you would not have asked the question in the first place.
I am going to guess at what you might mean.
[ 5(y-1)/21 ] / [ (y-1)/(33y) ]
5 (33y)/21 = 5(11y)/7 = (55/7) y
To divide and simplify the expression (5y - 5/21) / (y - 1/33y), we can follow a few steps:
Step 1: Simplify the expression within the numerator (5y - 5/21) and the expression within the denominator (y - 1/33y).
For the numerator, there are no common factors to factor out. However, we can combine the terms by finding a common denominator for (5y - 5) and 21. The common denominator would be 21, and we can write (5y - 5) as (5y * 21/21 - 5/21) = (105y/21 - 5/21) = (105y - 5)/21.
For the denominator, we can combine y and 1/33y by finding a common denominator, which would be 33y. We can write it as (y * 33y/33y - 1/33y) = (33y^2/33y - 1/33y) = (33y^2 - 1)/33y.
Step 2: Now, divide (5y - 5/21) by (y - 1/33y) by multiplying the numerator by the reciprocal of the denominator.
(105y - 5)/21 * (33y)/(33y^2 - 1)
= (105y * 33y - 5 * 33y)/(21 * (33y^2 - 1))
= (3465y^2 - 165y)/(693y^2 - 21)
Step 3: Simplify the expression if possible.
In this case, there is no common factor that can be factored out from both the numerator and the denominator. Therefore, the expression (3465y^2 - 165y)/(693y^2 - 21) cannot be simplified further.
Hence, the simplified form of (5y - 5/21) / (y - 1/33y) is (3465y^2 - 165y)/(693y^2 - 21).