Lesson 88: Multiplying and Dividing Rational Expressions — Practice Questions

1. 1. Multiply and simplify the expression: $(x^2 - 4x - 21) \cdot \frac{10}{5x + 15}$. The simplified product is ___.

2. 2. What is the simplified product of $\frac{x^2 - 4}{x^2 + 7x + 10} \cdot \frac{x+5}{x-2}$?

   • A. 1
   • B. $x+2$
   • C. $\frac{x-2}{x+5}$
   • D. $\frac{1}{x+2}$

3. 3. Multiply and simplify the expression: $\frac{5x^4}{6y^2} \cdot \frac{18y}{10x^2}$. The simplified expression is ___.

4. 4. Multiply and simplify the following expression: $\frac{6}{x^2 + x - 12} \cdot (x-3)$.

   • A. $\frac{6}{x+4}$
   • B. $\frac{6}{x-3}$
   • C. $6(x+4)$
   • D. $6$

5. 5. What is the simplified product of $\frac{x^2+2x-15}{1} \cdot \frac{7}{2x-6}$?

6. 6. Multiply and simplify the expression completely: $$\frac{5a^4}{2b} \cdot \frac{8b^3}{10a^2} = \_\_\_$$

7. 7. Simplify the expression: $$\frac{x+5}{x-1} \cdot \frac{x^2-1}{x^2-25}$$

   • A. $\frac{x+1}{x-5}$
   • B. $\frac{x-1}{x+5}$
   • C. $\frac{x-5}{x+1}$
   • D. 1

8. 8. Multiply the rational expressions and simplify the result: $$\frac{x^2-4x+4}{x+3} \cdot \frac{x+3}{x-2} = \_\_\_$$

9. 9. When simplifying the expression $\frac{x^2-9}{x+3}$, what is the correct and most crucial first step?

   • A. Cancel the $x$ terms because they appear on top and bottom.
   • B. Factor the numerator $x^2-9$ into $(x-3)(x+3)$.
   • C. Cancel the 9 and the 3 to get $\frac{x^2-3}{x+1}$.
   • D. Subtract $x$ from the numerator and denominator.

10. 10. Find the product and simplify: $$\frac{7m^5}{3n^2} \cdot \frac{6n}{14m^2} = \_\_\_$$