11. Partial fraction expansiona) i) Find roots of the denominator, ii) identify cases and iii) write the form of the partial fraction expan-sion (no need to determine coefficients) for the fractions below:s² +1A) F(s) =(s²+7s+12)(s² - 16)s+1B) F(s)=(5² +4s+13)(s² +9)²b) Find the partial fraction expansion of the following fraction with following steps i) write down theform of simple fractions and ii) determine coefficients.F(s)=-35³ +195² +(43+ A)s +34+5A(s² +7s+10)(s² +4s+4)where A is a real constant

According to the guideline, only one question with three subparts can be answered. Please repost other question separately. The given rational expression is F(s)=s2+1(s2+7s+12)(s2-16). The objectives are to calculate the roots of the denominator and the form of the partial fraction decomposition.The algebraic identity is a2-b2=(a-b)(a+b). Equate the denominator of the given expression with 0 and simplify. (s2+7s+12)(s2-16)=0s2+4s+3s+12s2-42=0s(s+4)+3(s+4)s2-42=0s+4s+3s+4s-4=0(s+4)2(s+3)(s-4)=0s=-4,-4,-3,4 Hence, the roots of the denominators are -4,-3,4. The multiplicity of -4 is two and the multiplicity of -3, 4 are one.The denominator of the given fraction can be written factored form as s+42s+3s-4. Thus, the partial fraction form of the given expression is As+4+B(s+4)2+Cs+3+Ds-4, where A, B, C, D are constants.