Final answer:
The least common denominator to solve the equation 1/x + (2/x)-3 = 5 is D. x(x-3), found by multiplying the distinct denominators x and x-3. Therefore, the correct answer is option D. x(x-3).
Step-by-step explanation:
The least common denominator (LCD) needed to solve the given equation 1/x + (2/x)-3 = 5 is obtained by finding the least common multiple (LCM) of the denominators. Since the denominators are x and x-3, the LCM is indeed x(x-3), since no other simpler multiple is common to both terms. Thus, the correct answer is D. x(x-3).
To find the LCD, each denominator is factored if necessary, and then each factor is used the greatest number of times it occurs in any of the denominators. Here, since 1/x and 2/(x-3) have no common factors and the denominators are already factored into primes, we simply multiply x by (x-3) without further simplification.