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Express the rational function in partial fractions.

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Step 1: Express the rational function in partial fractions.
We want to express 6x+1(x+1)(x+2)\frac{6x+1}{(x+1)(x+2)} in the form Ax+1+Bx+2\frac{A}{x+1} + \frac{B}{x+2}.

6x+1(x+1)(x+2)=Ax+1+Bx+2\frac{6x+1}{(x+1)(x+2)} = \frac{A}{x+1} + \frac{B}{x+2}

Multiply both sides by (x+1)(x+2)(x+1)(x+2) to clear the denominators:

6x+1=A(x+2)+B(x+1)6x+1 = A(x+2) + B(x+1)

To find AA, set x=−1x = -1:

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