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Write the Form of the Partial Fraction Decomposition of the Rational

Question 3

Multiple Choice

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants. x+5x(x2+6) 2\frac { x + 5 } { x \left( x ^ { 2 } + 6 \right) ^ { 2 } }


A) Ax+Bx+C(x2+6) 2\frac { A } { x } + \frac { B x + C } { \left( x ^ { 2 } + 6 \right) ^ { 2 } }
B) Ax+Bx2+6+Cx+D(x2+6) 2\frac { A x + B } { x ^ { 2 } + 6 } + \frac { C x + D } { \left( x ^ { 2 } + 6 \right) ^ { 2 } }
C) Ax+Bx+Cx2+6+Dx+E(x2+6) 2\frac { A } { x } + \frac { B x + C } { x ^ { 2 } + 6 } + \frac { D x + E } { \left( x ^ { 2 } + 6 \right) ^ { 2 } }
D) Ax+Bx+Cx+Dx2+6+Ex+F(x2+6) 2\frac { A x + B } { x } + \frac { C x + D } { x ^ { 2 } + 6 } + \frac { E x + F } { \left( x ^ { 2 } + 6 \right) ^ { 2 } }
E) Ax+Bx2+6+C(x2+6) 2\frac { A } { x } + \frac { B } { x ^ { 2 } + 6 } + \frac { C } { \left( x ^ { 2 } + 6 \right) ^ { 2 } }

Correct Answer:

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