After long-division, we have

Since (−4) − 4×8 = −16 < 0, the factor "x" − 4"x" + 8 is irreducible, and the partial fraction decomposition over the reals has the shape

Multiplying through by "x" − 4"x" + 8"x", we have the polynomial identity

Taking "x" = 0, we see that 16 = 8"A", so "A" = 2. Comparing the "x" coefficients, we see that 4 = "A" + "B" = 2 + "B", so "B" = 2. Comparing linear coefficients, we see that −8 = −4"A" + "C" = −8 + "C", so "C" = 0. Altogether,

The following example illustrates almost all the "tricks" one would need to use short of consulting a computer algebra system.

उदाहरण ३
विधि
उदाहरण २
उदाहरण ५ (limit method)