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Ans:-\frac{5 x^{2}+2}{\left(x^{2}-24 x+144\right)\left(x^{2}+3 x+4\right)}first we do factoring the denominator ento limar 5 x^{2}+2 Quadratic factors(x-12)^{2}\left(x^{2}+3 x+4\right)Step-2Now denominator hos (x-12)^{2} repeated linerr factor So This hes Partial fraction (sum of pouer tems) i.e.\frac{A}{x-12}+\frac{B}{(x-12)^{2}}Step-3 if denomehator hes qualratic form or x^{2}+3 x+4 tems then sum of Partial fractions includer a \operatorname{dem}\frac{C x+D}{x^{2}+3 x+4}Hence Partial Sraction is=\frac{5 x^{2}+2}{\left(x^{2}-2 x+144\right)\left(x^{2}+3 x+4\right)}=\frac{A}{x-12}+\frac{B}{(x-12)^{2}}+\frac{(x+D}{x^{2}+3 x+4}Note here we can not do limar fuctor of x^{2}+3 x+4 So we will use directiy as a non reducible factor, ...