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## Partial Fractions

Express rational functions as a sum of fractions with simpler denominators. You can apply this to telescoping series to mass cancel terms in a seemingly complicated sum.

# Cover Up Rule

By the coverup rule, the coefficient of the term $$\frac{1}{ x + 6 }$$ in the partial fraction decomposition of

$\frac{ 1} { ( x + 6 ) ( x + 19 ) },$

has the form $$\frac{1}{A}$$. What is $$A$$?

By the coverup rule, the coefficient of the term $$\frac{1}{ x + 2 }$$ in the partial fraction decomposition of

$\frac{ 1} { ( x - 2 ) ( x + 2 ) ( x + 7 ) },$

has the form $$\frac{1}{A}$$. What is $$A$$?

By the coverup rule, the coefficient of the term $$\frac{1}{ x + 4 }$$ in the partial fraction decomposition of

$\frac{ 1} { ( x + 4 ) ( x^2 + 5 x + 20 ) },$

has the form $$\frac{1}{A}$$. What is $$A$$?

By the coverup rule, the coefficient of the term $$\frac{1}{ x + 2 }$$ in the partial fraction decomposition of

$\frac{ 1} { ( x + 2 ) ( x^2 + 4 x + 28 ) },$

has the form $$\frac{1}{A}$$. What is $$A$$?

By the coverup rule, the coefficient of the term $$\frac{1}{ x + 3 }$$ in the partial fraction decomposition of

$\frac{ 1} { ( x + 3 ) ( x + 9 )(x+16) },$

has the form $$\frac{1}{A}$$. What is $$A$$?

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