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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.

Partial Fractions - Linear Factors

If the following is an identity in $$x$$: $\frac{A}{(x-2)(5x-8)}=\frac{1}{x-2}-\frac{B}{5x-8},$ what is the value of $$A+B?$$

How many terms would there be in the partial fraction decomposition of

$\frac{1}{ ( x- 5) ( x + 5) ( x + 9 )}?$

If the following is an identity in $$x$$:

$\frac{11x+50 }{(x+2)(x+6)} = \frac{A}{x+2} + \frac{B}{x+6},$

what is the value of $$A + B?$$

Which of the following is the correct partial fraction decomposition of

$\frac{ x+1 } { ( x + 2) ( x + 3) } ?$

If the following is an identity in $$x$$: $\frac{5x-6}{x^2-3x+2}=\frac{a}{x-1}+\frac{b}{x-2},$ what is the value of $$a \times b$$?

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