Question

Solve for x and simplify the answer fully.

2/x-3 = 5/x-3

Answer 1

To solve the equation \( \frac{2}{x-3} = \frac{5}{x-3} \), we first notice that both sides of the equation involve the same denominator, \( x - 3 \). We can eliminate the denominators by multiplying both sides of the equation by \( x - 3 \), provided that \( x \neq 3 \) to avoid division by zero:

\[
2 = 5
\]

This result is a contradiction and indicates that \( 2 \) does not equal \( 5 \). Therefore, there is no solution for \( x \) that satisfies the equation.

In conclusion, the solution to the equation \( \frac{2}{x-3} = \frac{5}{x-3} \) is **no solution**.