Question

resolve into portial fractions x²+x+2/x²(x²+3)²​

Answer 1

\left[x _{1}\right] = \left[ \frac{-1}{4}+\frac{ - \sqrt{\left( \frac{-13}{12}+\frac{76\,\sqrt[3]{2}}{3\,\sqrt[3]{\left( -686+\left( 18\,i \right) \,\sqrt{3967}\right) }}+\frac{\sqrt[3]{\left( -686+\left( 18\,i \right) \,\sqrt{3967}\right) }}{3\,\sqrt[3]{2}}\right) }}{2}+\frac{ - \sqrt{\left( \frac{-13}{6}+\frac{\left( -76\right) \,\sqrt[3]{2}}{3\,\sqrt[3]{\left( -686+\left( 18\,i \right) \,\sqrt{3967}\right) }}+\frac{ - \sqrt[3]{\left( -686+\left( 18\,i \right) \,\sqrt{3967}\right) }}{3\,\sqrt[3]{2}}+\frac{-7}{4\,\sqrt{\left( \frac{-13}{12}+\frac{76\,\sqrt[3]{2}}{3\,\sqrt[3]{\left( -686+\left( 18\,i \right) \,\sqrt{3967}\right) }}+\frac{\sqrt[3]{\left( -686+\left( 18\,i \right) \,\sqrt{3967}\right) }}{3\,\sqrt[3]{2}}\right) }}\right) }}{2}\right][x​1​​]=​⎣​⎢​⎢​⎢​⎢​⎢​⎢​⎢​⎢​⎢​⎢​⎢​⎢​⎢​⎢​⎢​⎢​⎡​​​4​​−1​​+​2​​−√​(​12​​−13​​+​3​3​​√​(−686+(18i)√​3967​​​)​​​​​76​3​​√​2​​​​​+​3​3​​√​2​​​​​​3​​√​(−686+(18i)√​3967​​​)​​​​​)​​​​​+​2​​−​⎷​​​​​​​​​​​​⎝​⎜​⎜​⎜​⎜​⎛​​​6​​−13​​+​3​3​​√​(−686+(18i)√​3967​​​)​​​​​(−76)​3​​√​2​​​​​+​3​3​​√​2​​​​​−​3​​√​(−686+(18i)√​3967​​​)​​​​​+​4√​(​12​​−13​​+​3​3​​√​(−686+(18i)√​3967​​​)​​​​​76​3​​√​2​​​​​+​3​3​​√​2​​​​​​3​​√​(−686+(18i)√​3967​​​)​​​​​)​​​​​−7​​​⎠​⎟​⎟​⎟​⎟​⎞​​​​​​​​⎦​⎥​⎥​⎥​⎥​⎥​⎥​⎥​⎥​⎥​⎥​⎥​⎥​⎥​⎥​⎥​⎥​⎤​​