Final answer:
To solve the equation, find a common denominator, simplify the expression, combine the numerators, and solve for x.
Step-by-step explanation:
To solve the rational expression -8/x + 2x+1/2x = 1/2, we need to find a common denominator and simplify the expression. The common denominator is 2x, so we multiply the first fraction by 2/2 and the second fraction by x/x. This gives us:
-16/2x + (2x+1)/(2x) = 1/2
Next, combine the numerators of the fractions on the left side: -16 + 2x + 1 = 1/2.
Simplifying further, we get: -16 + 2x + 1 = 1/2
Combine like terms: 2x - 15 = 1/2
Finally, solve for x: 2x = 1/2 + 15
2x = 15.5
x = 7.75