Question

Which partial-fraction decomposition is appropriate for \[\frac{\mathrm{p}x+\mathrm{q}}{(x-\mathrm{a})(x-\mathrm{b})}\]?

Options

• \[\frac{\mathrm{A}}{(x-\mathrm{a})}+\frac{\mathrm{B}}{(x-\mathrm{a})^{2}}\]

• \[\frac{\mathrm{A}}{x-\mathrm{a}}+\frac{\mathrm{B}}{x-\mathrm{b}}\]

• \[\frac{\mathrm{A}x+\mathrm{B}}{(x-\mathrm{a})(x-\mathrm{b})}\]

• \[\frac{\mathrm{A}}{x-\mathrm{a}}+\frac{\mathrm{B}x+\mathrm{C}}{x^{2}+\mathrm{b}x+\mathrm{c}}\]

Answer 1

The denominator has the non-repeated linear factors \[(x-\mathrm{a})\] and \[(x-\mathrm{b})\]. Each distinct linear factor receives a constant numerator.