Final answer:
To find the simplified form of an algebraic expression, one must distribute coefficients, combine like terms, and simplify fractions. For example, the simplified form of (1/2x^2 - 4x) + x^2 is (3/2x^2 - 4x).
Step-by-step explanation:
The student is requesting the simplified form of an algebraic expression. To simplify an algebraic expression, you should combine like terms and make sure that the expression is in its simplest form, which means that there are no parentheses left, and all like terms have been combined.
Looking at the given options:
a) (1/2x^2 - 4x) + 2/x
b) (1/2x^2 - 8x) + 2/x
c) (1/2x^2 - 2x) + 2/x
d) (1/2x^2 - 4x) + x^2
If you are asked to simplify one of these, you would need to distribute any coefficients, combine like terms, and simplify any fractions if possible. For instance:
For option d) (1/2x^2 - 4x) + x^2, to simplify, combine the like terms 1/2x^2 and x^2:
(1/2x^2) + x^2 = (1/2 + 1)x^2 = (1.5)x^2 = 3/2x^2
Then combine the result with the rest of the expression:
(3/2x^2 - 4x)
This would be the simplified form of option d).