Partial Fractions Calculator
Decompose rational expressions into partial fractions for easier integration and simplification.
Sisesta ratsionaalavaldis
Näide: (x + 1)*(x + 2) nimetaja jaoks
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Osaliste murdude lagundamine
Osaliste murdude lagundamine on meetod keeruliste ratsionaalavaldiste lagundamiseks lihtsamateks murdudeks. See tehnika on eriti kasulik integreerimisel.
Meetod
Lineaarsete tegurite puhul: Jagage murd lihtsamateks murdudeks
\(\frac{P(x)}{(x-a)(x-b)} = \frac{A}{x-a} + \frac{B}{x-b}\)Näide
\(\frac{5x + 7}{(x+1)(x+2)} = \frac{A}{x+1} + \frac{B}{x+2}\)\(5x + 7 = A(x+2) + B(x+1)\)\(\text{Solving: } A = 2, B = 3\)\(\frac{5x + 7}{(x+1)(x+2)} = \frac{2}{x+1} + \frac{3}{x+2}\)