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10 cards from this deck
A function of the form p(x)/q(x)p(x)/q(x)p(x)/q(x) with polynomials.
Use polynomial factorization and cancel common factors.
f(x)=x2+5x−8f(x) = \frac{x^2 + 5}{x - 8}f(x)=x−8x2+5 is a rational function.
Write the expression as a sum of simpler fractions.
Perform polynomial long division before finding partial fractions.
Use strategic values of xxx to simplify the equations.
2(x+1)(x+3)=1x+1−1x+3\frac{2}{(x+1)(x+3)} = \frac{1}{x+1} - \frac{1}{x+3}(x+1)(x+3)2=x+11−x+31.
1x2−1=12(x−1)−12(x+1)\frac{1}{x^2-1} = \frac{1}{2(x-1)} - \frac{1}{2(x+1)}x2−11=2(x−1)1−2(x+1)1.
Use A/(x−1)+B/(x−1)2+C/(x−2)A/(x-1) + B/(x-1)^2 + C/(x-2)A/(x−1)+B/(x−1)2+C/(x−2).
Combine to 11−x(3−x)(1+x)\frac{11-x}{(3-x)(1+x)}(3−x)(1+x)11−x.
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