Divide and state the quotient in simplest form
5y/y^2+4y+4 ÷ 20y^2/y^2-4
To divide these two rational expressions, you can follow these steps:
1. Rewrite the division as multiplication by flipping the second fraction:
(5y)/(y^2 + 4y + 4) * (y^2 - 4)/(20y^2)
2. Factor the denominators and simplify the expressions:
(5y)/((y + 2)^2) * ((y - 2)(y + 2))/(20y^2)
3. Rewrite the multiplication using the factored terms:
(5y)/((y + 2)^2) * (y - 2)(y + 2)/(20y^2)
4. Cancel out common factors in the numerator and denominator:
5/(y + 2) * (y - 2)/20
5. Multiply out the fractions:
(5y - 10)/(20y + 40)
6. Simplify the final expression:
(5y - 10)/(20y + 40) can be further simplified by factoring out 5 in the numerator and 20 in the denominator:
5(y - 2)/20(y + 2)
7. Divide the coefficients by their greatest common divisor, which is 5:
(y - 2)/(4(y + 2))
Therefore, the quotient of the given expressions in simplest form is (y - 2)/(4(y + 2)).