1.11 Partial fractions Quiz

1. $\frac{x+7}{(x-1)(x+3)} \equiv \frac{A}{x-1} + \frac{B}{x+3}$. Find $A$.

• A. $2$
• B. $-1$
• C. $8$
• D. $\frac{7}{3}$

2. For the same expression, find $B$.

• A. $1$
• B. $-1$
• C. $2$
• D. $-4$

3. Which of these can be written in partial fractions using the IB method?

• A. $\frac{x^2+1}{(x-1)(x+2)}$
• B. $\frac{3}{(x-1)^2}$
• C. $\frac{2x-1}{(x+4)(x-3)}$
• D. $\frac{x}{x^2+1}$

4. Express $\frac{6}{x(x+3)}$ in partial fractions.

• A. $\frac{2}{x} - \frac{2}{x+3}$
• B. $\frac{6}{x} - \frac{6}{x+3}$
• C. $\frac{2}{x} + \frac{2}{x+3}$
• D. $\frac{3}{x} - \frac{3}{x+3}$

5. Find $\sum_{r=1}^{9}\frac{1}{r(r+1)}$.

• A. $\frac{1}{10}$
• B. $\frac{9}{10}$
• C. $\frac{10}{11}$
• D. $1$