[latex] frac{-(z ^{2}-2z+4)(2z ^{2} +z) }{(4z ^{2} -1)(z ^{3} +8)} = frac{-(z ^{2}-2z+4)*z*(2z +1) }{(2z-1)(2z+1)(z+2)(z ^{2} -2z+4)} = \ \ = frac{-1*z*1}{(2z-1)*(z+2)*1} =- frac{z}{2z ^{2}+4z-z-2 } =- frac{z}{2z ^{2}+3z-2 } [/latex]