Question

Simplify the expression (1/2x^2 - 4x) + 2/x.

a) (1/2x^2 - 4x) + 2/x
b) (1/2x^2 - 4x) + 2x
c) (1/2x^2 - 8x) + 2/x
d) (1/2x^2 - 2x) + 2/x

Answer 1

To simplify the expression (1/2x^2 - 4x) + 2/x, find a common denominator and combine the numerators to get (x+4x^3+4x^2)/(2x^2).

Step-by-step explanation:

To simplify the expression (1/2x^2 - 4x) + 2/x, we need to combine like terms. In this case, the like terms are the terms with x in the denominator. So, we can rewrite the expression as (1/2x^2 - 4x) + (2/x). Now, we can find a common denominator, which is 2x^2, and combine the numerators:

(1/2x^2 - 4x) + (2/x) = (x/x)(1/2x^2 - 4x) + (2/x)(2x^2/2x^2) = (x+4x^3)/(2x^2) + 4x^2/(2x^2) = (x+4x^3+4x^2)/(2x^2)

So, the simplified expression is (x+4x^3+4x^2)/(2x^2).