27y/y^2-1• y^2+y/36y^2 state the product in simplest form
To find the product of the given expression in simplest form, we need to multiply the two fractions together.
(27y / y^2 - 1) • (y^2 + y / 36y^2)
= (27y/y^2 - 1) • ((y^2 + y) / 36y^2)
= (27/y - 1/y^2) • ((y^2 + y) / 36y^2)
Now, let's simplify this expression by multiplying the numerators and denominators separately:
(27 • (y^2 + y)) / (36y • y^2) - (y^2 + y) / 36y^2
= (27y^2 + 27y) / (36y^3) - (y^2 + y) / 36y^2
To find a common denominator, we multiply the first fraction by y/y, and the second fraction by y/36:
= (27y^2 + 27y) / (36y^3) - (y^3 + y^2) / 36y^3
Now that we have a common denominator, we can combine the fractions:
= (27y^2 + 27y - y^3 - y^2) / 36y^3
= (26y^2 + 27y) / 36y^3
Therefore, the product of the given expression in simplest form is (26y^2 + 27y) / 36y^3.