Multiply. State the product in simplest form. (27y)/(y²-1)*(y²+y)/(36y²)
To find the product, first simplify the expression by factoring the denominators:
y² - 1 can be factored as (y - 1)(y + 1)
y² + y can be factored as y(y + 1)
Now, the expression becomes:
(27y) / [(y - 1)(y + 1)] * [y(y + 1)] / (36y²)
Now, multiply the numerators and denominators:
(27y * y(y + 1)) / [(y - 1)(y + 1)(36y²)]
= (27y²(y + 1)) / [(y - 1)(y + 1)(36y²)]
= (27y²(y + 1)) / [36y²(y - 1)]
Now, simplify the expression by canceling out common factors in the numerator and denominator:
= (27(y + 1)) / 36(y - 1)
= (9(y + 1)) / 12(y - 1)
Therefore, the product in simplest form is (9(y + 1)) / 12(y - 1) or (3(y + 1)) / 4(y - 1)