Why is there no solution to the equation 3/(x-2)=5/(x-2)

Answer 1

There is no solution here because both denominators contain an unknown variable x, and -2. Each fraction also contains a different numerator. Therefore, if you were to plug in any single whole number for x in both fractions, the denominator(s) would be the same, but when divided by different numerators accordingly, you would get two different answers that would subsequently be unequal to each other. And as shown in the math exercise above, the final answer(s) on both sides of the equation need to be equal. Even if the denominators both totaled zero—by plugging in 2 for x, and subtracting 2 to equal zero (2-2=0), zero divided by any number is no solution.

Hence, this equation has no solution.