Partial fractions Quiz

1. What is the form of $\dfrac{3x+1}{(x-2)^2}$ in partial fractions?

• A. $\dfrac{A}{(x-2)^2}$
• B. $\dfrac{A}{x-2}+\dfrac{B}{(x-2)^2}$
• C. $\dfrac{A}{x-2}+\dfrac{B}{x-2}$
• D. $\dfrac{Ax+B}{(x-2)^2}$

2. Find $A$: $\dfrac{4}{(x-1)(x+3)}\equiv\dfrac{A}{x-1}+\dfrac{B}{x+3}$.

• A. $4$
• B. $-1$
• C. $-4$
• D. $1$

3. For $\dfrac{x+5}{(x+1)(x+3)}\equiv\dfrac{A}{x+1}+\dfrac{B}{x+3}$, find $B$.

• A. $-1$
• B. $2$
• C. $1$
• D. $-2$

4. Which value of $x$ is substituted to find $A$ in $\dfrac{A}{3x+2}$?

• A. $x=\frac23$
• B. $x=-\frac23$
• C. $x=-\frac32$
• D. $x=\frac32$

5. $\dfrac{2}{x}-\dfrac{2}{x+2}$ as a single fraction is:

• A. $\dfrac{2}{x(x+2)}$
• B. $\dfrac{0}{x+2}$
• C. $\dfrac{4}{x(x+2)}$
• D. $\dfrac{4}{x+2}$