Partial Fractions Calculator
Decompose rational expressions into partial fractions for easier integration and simplification.
Sisesta ratsionaalne avaldis
Näide: (x + 1)*(x + 2) nimetaja jaoks
Theory & Formula
Osaosaliste murru lahutamine
Osaosaliste murru lahutamine on meetod keerukate ratsionaalsete avaldiste lihtsustamiseks. See tehnika on eriti kasulik integreerimisel.
Meetod
Lineaarsete tegurite jaoks: Jaga murd lihtsamate murru summaks
\(\frac{P(x)}{(x-a)(x-b)} = \frac{A}{x-a} + \frac{B}{x-b}\)Näide
\(\frac{5x + 7}{(x+1)(x+2)} = \frac{A}{x+1} + \frac{B}{x+2}\)\(5x + 7 = A(x+2) + B(x+1)\)\(\text{Solving: } A = 2, B = 3\)\(\frac{5x + 7}{(x+1)(x+2)} = \frac{2}{x+1} + \frac{3}{x+2}\)