Step 1 :Given the equation: \(\frac{4x+5}{(x-5)(x+3)} = \frac{A}{x-5} + \frac{B}{x+3}\)
Step 2 :Clear the denominators by multiplying both sides by \((x-5)(x+3)\): \(4x+5 = A(x+3) + B(x-5)\)
Step 3 :Solve for A and B:
Step 4 :Final Answer: \(A = \boxed{\frac{25}{8}}\) and \(B = \boxed{\frac{7}{8}}\)