9 over y + 2 over 5 + 3 over 5y
To simplify the expression 9/y + 2/5 + 3/5y, we need to find a common denominator for the fractions.
Step 1: Find the common denominator
The denominators are y, 5, and 5y. To find the least common denominator, we can multiply the individual denominators together: y * 5 * 5y = 25y^2.
Step 2: Convert each fraction with the common denominator
To convert the first fraction, 9/y, to an equivalent fraction with the common denominator 25y^2, we multiply the numerator and denominator by (5 * 5y):
(9/y) * (5 * 5y)/(5 * 5y) = (45y)/(5y^2).
To convert the second fraction, 2/5, to an equivalent fraction with the common denominator 25y^2, we multiply the numerator and denominator by (y * 5y):
(2/5) * (y * 5y)/(y * 5y) = (2y^2)/(5y^2).
To convert the third fraction, 3/5y, to an equivalent fraction with the common denominator 25y^2, we multiply the numerator and denominator by (5y^2):
(3/5y) * (5y^2)/(5y^2) = (15y)/(25y^2).
Now, we can rewrite the expression with the common denominator 25y^2:
(45y)/(5y^2) + (2y^2)/(5y^2) + (15y)/(25y^2)
Step 3: Simplify the expression
Combine the numerators into a single fraction:
(45y + 2y^2 + 15y)/(25y^2)
Simplify the numerator:
(2y^2 + 60y)/(25y^2)
The simplified expression is (2y^2 + 60y)/(25y^2).