Which form of partial fractions fits (x + 2)/((x - 1)^2(x + 3))?

A/(x - 1) + B/((x - 1)^2) + C/(x + 3)

(Ax + B)/((x - 1)^2) + C/(x + 3)

Question 62

EasyOriginal question

Which form of partial fractions fits $\frac{x + 2}{(x - 1)^{2}(x + 3)}$ ?

\frac{A}{(x - 1)^{2}} + \frac{B}{x + 3}

Correct answerYour answer

\frac{A}{x - 1} + \frac{B}{x + 3}

Correct answerYour answer

\frac{Ax + B}{(x - 1)^{2}} + \frac{C}{x + 3}

Correct answerYour answer

\frac{A}{x - 1} + \frac{B}{(x - 1)^{2}} + \frac{C}{x + 3}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

A repeated factor $(x - 1)^{2}$ needs a term for each power: $\frac{A}{x - 1}$ and $\frac{B}{(x - 1)^{2}}$ .
The factor $x + 3$ gets its own $\frac{C}{x + 3}$ .

Worth noting

Keeping only $\frac{A}{(x - 1)^{2}}$ leaves too few constants to match every numerator.

Ten questions from Indefinite Integrals, at your own pace.