Question

Which partial-fraction decomposition is used for \[\frac{\mathrm{p}x+\mathrm{q}}{(x-\mathrm{a})^{2}}\]?

Options

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

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

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

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

Answer 1

For a repeated linear factor, every power is included separately. Hence both \[\frac{\mathrm{A}}{x-\mathrm{a}}\] and \[\frac{\mathrm{B}}{(x-\mathrm{a})^{2}}\] are required.