Question #N562
For what value of $x$ does the equation $\frac{x+5}{x-2} = \frac{x+2}{x-4}$ have a solution?
A. -1
B. 2
C. 4
D. 7
Correct Answer is: D
To solve for x, we can cross-multiply: $(x+5)(x-4) = (x+2)(x-2)$. Expanding both sides, we get $x^2 + x - 20 = x^2 - 4$. Subtracting $x^2$ from both sides, we get $x - 20 = -4$. Adding 20 to both sides, we get $x = 16$. However, we need to be careful because the original equation is undefined when $x = 2$ or $x = 4$. Since 16 is not equal to 2 or 4, the solution to the equation is $x = 16$.