Final answer:
The fractions in the equation x/2 = 3 + (x - 5)/5 can be eliminated by multiplying both sides by the least common denominator (LCD), which is 10. To find the LCD, you multiply the prime denominators 2 and 5 to get 10. Then, multiply both sides by 10 to eliminate the fractions and solve for x.
Step-by-step explanation:
The fractions in the equation x/2 = 3 + (x - 5)/5 can be eliminated by multiplying both sides by the least common denominator (LCD) of x/2 and (x - 5)/5, which is 10.
To find the LCD, we look at the denominators 2 and 5. Since 2 and 5 are both prime numbers, their LCD is simply their product. Therefore, the LCD of x/2 and (x - 5)/5 is 2 × 5 = 10.
Once we have identified the LCD, we multiply both sides of the equation by this number to eliminate the fractions. Doing so, we would get 10 × (x/2) = 10 × (3 + (x - 5)/5). Simplification on both sides of the equation would then allow us to solve for x without dealing with fractions.