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Write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the constants. $$\frac { 4 x ^ { 3 } + 7 x ^ { 2 } } { ( x ^ { 2 } + 5 ) ^ { 2 } }$$ What is the form of the partial decomposition of the given expression?
Answer: $$\frac { 4 x ^ { 3 } + 7 x ^ { 2 } } { ( x ^ { 2 } + 5 ) ^ { 2 } } = \frac { 4 x + 7 } { x ^ { 2 } + 5 } + \frac { - 20 x - 35 } { ( x ^ { 2 } + 5 ) ^ { 2 } }$$