Rational expressions and algebraic division Quiz

1. Simplify $\dfrac{x^2-4}{x^2+x-6}$.

• A. $\dfrac{x+2}{x-3}$
• B. $\dfrac{x-2}{x+3}$
• C. $\dfrac{x+2}{x+3}$
• D. $\dfrac{-4}{x-6}$

2. Simplify $\dfrac{x+2}{x^2+5x+6}$.

• A. $\dfrac{1}{x+3}$
• B. $\dfrac{1}{x+2}$
• C. $\dfrac{1}{5x+6}$
• D. $x+3$

3. Write $\dfrac{1}{x-1}-\dfrac{1}{x+1}$ as a single fraction.

• A. $0$
• B. $\dfrac{2x}{x^2-1}$
• C. $\dfrac{-2}{x^2-1}$
• D. $\dfrac{2}{x^2-1}$

4. When $x^2+5x+7$ is divided by $(x+2)$, what are the quotient and remainder?

• A. quotient $x+3$, remainder $0$
• B. quotient $x+3$, remainder $1$
• C. quotient $x+2$, remainder $3$
• D. quotient $x+7$, remainder $1$

5. Simplify $\dfrac{2x^2+3x-5}{x-1}$.

• A. $2x-5$
• B. $2x+3$
• C. $2x+5$
• D. $x+5$