Final answer:
To simplify the given expression, combine like terms by adding coefficients of the same power of x, which results in (27/4)x^2 - 2/3x + 7/4. The correct answer is A) Combine like terms and simplify.
Step-by-step explanation:
To simplify the expression (3/4x^2 + 5/4) + (6x^2 - 2/3x + 1/2), follow these steps:
- Combine like terms by adding or subtracting coefficients of the same power of x.
- Start by combining the x^2 terms: (3/4)x^2 + 6x^2 = (3/4 + 24/4)x^2 = (27/4)x^2.
- Next, combine the x terms: Since there is only one x term, -2/3x, we keep it as it is.
- Finally, combine the constant terms: 5/4 + 1/2 = (5/4 + 2/4) = (7/4).
- You now have (27/4)x^2 - 2/3x + 7/4 as the simplified expression.
Therefore, the correct action is to combine like terms and simplify (Option A).
Remember to check the answer to see if it is reasonable. In this case, all like terms have been combined, and the expression is in its simplest form.