Solve $\frac{8}{x+3}+\frac{3}{x+8}=1$

Step 1 ：\(\frac{8}{x+3} + \frac{3}{x+8} = 1\)

Step 2 ：Find a common denominator: \((x+3)(x+8)\)

Step 3 ：\(\frac{8(x+8) + 3(x+3)}{(x+3)(x+8)} = 1\)

Step 4 ：\(8x + 64 + 3x + 9 = (x+3)(x+8)\)

Step 5 ：\(11x + 73 = x^2 + 11x + 24\)

Step 6 ：\(x^2 - 49 = 0\)

Step 7 ：\(x^2 = 49\)

Step 8 ：\(x = \pm\sqrt{49}\)

Step 9 ：\boxed{x = -7, 7}