What is the solution to x+2/x-3 = 5/x-3?

Both fractions share the denominator $x - 3$, so multiply through by it: $x + 2 = 5$, giving $x = 3$. But $x = 3$ makes the denominator $x - 3$ equal to zero in the original equation, so the expression is undefined and the value is extraneous. With no valid candidate left, there is no solution, choice D. Choice A ($x = 3$) is the extraneous value that should be rejected. Choice B ($x = 5$) copies the right-hand numerator. Choice C ($x = -2$) comes from setting the numerator $x + 2$ equal to zero. Always check for excluded values after clearing denominators.