subtract. simplify your answer.
1/6y²+24y - 3/y²-y-20
To subtract and simplify the expression (1/6y^2 + 24y) - (3/y^2 - y - 20), follow these steps:
Step 1: Combine like terms within each polynomial
Within the first polynomial, we have the terms 1/6y^2 and 24y. There are no like terms within the second polynomial, as it is already in simplified form. So, we do not need to combine any terms within the second polynomial.
Step 2: Distribute the negative sign to the terms inside the second parentheses
Since we have a subtraction sign in front of the second parentheses, we need to distribute the negative sign to all the terms inside. So, we change the signs of each term inside the second parentheses, resulting in -3/-y^2 + y + 20.
Step 3: Combine like terms across the subtraction
Now, we can combine like terms across the subtraction. In this case, we have terms with the same exponent: 1/6y^2 and -3/-y^2. By combining these terms, we get (1/6y^2 + 3/y^2).
Step 4: Combine like terms within the resulting expression
Finally, we have (1/6y^2 + 3/y^2) + 24y + y + 20. Within this expression, we have the terms 1/6y^2 and 3/y^2, which have the same denominator. To add or subtract fractions, we need a common denominator. In this case, the common denominator is 6y^2. We can rewrite the expression as (1/6y^2 + 3/6y^2) + 24y + y + 20.
Step 5: Add the fractions and combine like terms
Now, we can add the fractions (1/6y^2 + 3/6y^2), which gives us 4/6y^2. Simplifying this fraction further, we get 2/3y^2. Therefore, our final simplified expression is 2/3y^2 + 24y + y + 20.
Remember, always double-check your work to ensure accuracy.