Partial Fractions

The decomposition theorem

Long division first

Irreducible quadratics and repeated factors

A full example

Before decomposing into partial fractions, a rational function must satisfy which condition?

To find A and B in the decomposition of (3x + 5)/((x - 1)(x + 3)), which method is fastest?

A partial fraction (Bx + C)/(x^2 + 4) integrates to which pair of terms?

The denominator (x - 1)^2 contributes which partial fraction structure?

The shortcut of substituting each factor's root to isolate coefficients is known by which name?

The partial fraction A/(ax + b) integrates to what kind of function? Answer with one word.

A quadratic denominator x^2 + 2x + 5 is irreducible. Which completed form enables its partial fraction's integration?

The partial fraction over an irreducible quadratic integrates to a logarithm plus which other function? Answer with one word.

Dividing x^2 by x + 1 gives quotient x - 1 and remainder 1. How many terms does the decomposition of the proper remainder have over the single linear factor? Answer with a number.

Clearing denominators in 3x + 5 = A(x + 3) + B(x - 1) and substituting x = 1 gives 8 = 4A. What is A? Answer with a number.