Final answer:
The simplified result of the subtraction (5)/(12wy^3) - (3)/(8w^2y) is (10w - 9)/(24w^2y).
Step-by-step explanation:
The student asked to subtract two fractions with variables and simplify the result: (5)/(12wy^3) - (3)/(8w^2y). To subtract these fractions, we need a common denominator. Since 12wy^3 and 8w^2y are the denominators, we can observe that the least common multiple (LCM) would be 24w^2y^3. Multiplying the fractions by an appropriate form of 1 to get this common denominator, we would have:
- The first fraction becomes (5)/(12wy^3) × (2wy^2)/(2wy^2) = (10wy^2)/(24w^2y^3).
- The second fraction becomes (3)/(8w^2y) × (3y^2)/(3y^2) = (9y^2)/(24w^2y^3).
Now we can subtract them:
(10wy^2)/(24w^2y^3) - (9y^2)/(24w^2y^3) = (10wy^2 - 9y^2)/(24w^2y^3)
After subtraction, we can simplify:
(y^2(10w - 9))/(24w^2y^3)
Cancel out the y^2 term from the numerator and denominator:
(10w - 9)/(24w^2y)
So, the simplified result is (10w - 9)/(24w^2y).