Algebraic Fractions Quiz

1. Which step must always come first when simplifying an algebraic fraction?

• A. Cancel the $x$ terms
• B. Factorise the numerator and denominator
• C. Multiply out the brackets
• D. Add the numerator and denominator

2. What is required before adding two algebraic fractions with different denominators?

• A. A common denominator
• B. Equal numerators
• C. Factorising the numerators only
• D. Cross-multiplying immediately

3. How do you divide by an algebraic fraction?

• A. Add the reciprocal
• B. Multiply by the reciprocal of the second fraction
• C. Subtract the denominators
• D. Square both fractions

4. Simplify $\dfrac{x^2-9}{x^2+5x+6}$

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

5. When solving $\dfrac{3}{x} + \dfrac{2}{x-1} = 1$, which values of $x$ must be rejected even if they satisfy the resulting quadratic?

• A. $x=1$ and $x=2$
• B. $x=0$ and $x=1$
• C. $x=-1$ and $x=0$
• D. There are no restrictions