Step 1 :Given expression: \(\frac{40-\sqrt{180}}{4\sqrt{5}-3}\)
Step 2 :Rewrite \(\sqrt{180}\) as \(6\sqrt{5}\): \(\frac{40-6\sqrt{5}}{4\sqrt{5}-3}\)
Step 3 :Multiply the numerator and denominator by the conjugate of the denominator: \(\frac{(40-6\sqrt{5})(4\sqrt{5}+3)}{(4\sqrt{5}-3)(4\sqrt{5}+3)}\)
Step 4 :Simplify the expression: \(2\sqrt{5}\)
Step 5 :\(\boxed{2\sqrt{5}}\) is the final answer