Consider the setup of this partial fraction decomposition: \frac{x^{2}+6}{x\left(x^{2}-5x-6\right)}=\frac{A}{x}\ +\ \frac{Bx+C}{x^{2}-5x-6} The setup of this problem is incorrect, but does it give the correct answer despite the error? Explain the error in setup, solve the problem with this setup, and then correct the error and solve the problem with the correct setup. Did you get the same answer with each setup?

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6. (12 pts) Consider the setup of this partial fraction decomposition:

\frac{x ^{2} + 6}{x ( x ^{2} ? 5 x ? 6 )} = \frac{A}{x} + \frac{B x + C}{x ^{2} ? 5 x ? 6}

The setup of this problem is incorrect, but does it give the correct answer despite the error? Explain the error in setup, solve the problem with this setup, and then correct the error and solve the problem with the correct setup. Did you get the same answer with each setup?

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