Final answer:
Subtracting the fractions (x-3)/(2x)-(x+3)/(2x) involves subtracting the numerators and simplifying the result, yielding a final answer of -3/x.
Step-by-step explanation:
To subtract fractions with the same denominator, you subtract the numerators and keep the same denominator. In this case, both fractions have the denominator 2x. The equation is ((x-3)/(2x)) - ((x+3)/(2x)). You subtract the numerators to get (x-3)-(x+3). This simplifies to x-3-x-3, which further simplifies to -6.
So, the resulting fraction after subtracting and simplifying is -6/(2x). Note how in the subtraction of numerators, the x terms cancel each other out, leaving only the constants -3 and -3 to be subtracted. Writing the final simplified form, we divide -6 by the common factor 2, yielding the most reduced answer -3/x.