6y/y^2+y-72 divided by y^6/x-y
6y/(y^2+y-72)
---------------
y^6/(x-y)
6y/((y+9)(y-8)) * (x-y)/y^6
6(x-y)/(y^5 (y+9)(y-8))
To simplify the expression (6y/y^2+y-72) / (y^6/x-y), we can follow these steps:
Step 1: Factorize the numerator and the denominator separately.
The numerator 6y can be written as 2 * 3 * y.
The denominator y^6/x-y can be written as (y * y * y * y * y * y) / (x - y).
Step 2: Simplify the expression by canceling out common factors.
In the numerator, the y in 2 * 3 * y can be canceled with one of the y's in the denominator (y * y * y * y * y * y). This leaves us with (2 * 3) / (y * y * y * y) = 6 / (y^4).
The simplified expression is now 6 / (y^4).