Dividing rational expressions

Lessons

• Introduction
  $\bullet$ Review: Dividing Monomials

---

• 1.
  Simplifying Rational Expressions Involving Division
  State the restrictions on the variables, then simplify.
  $\frac{81x}{64y^2} \div \frac{27x^2}{32y}$

---

• 2.
  Simplifying Rational Expressions Involving both Multiplication and Division
  State the restrictions on the variables, then simplify.
  
  a)

  $\frac{72x^4y^2}{8x^5z^3} \times \frac{y^2}{x^3} \div \frac{15x^4y^4}{15z^4}$
  
  
  b)

  $\frac{15x^4y^4}{18x^2z^7} \times \frac{5z^3}{5x^3y} \div \frac{25x^2y}{50z^5}$
  
  

---

• 3.
  Dividing Rational Expressions in Factored Form
  State the non-permissible values for x, then simplify:
  $\frac{(x+2)}{(x-5)(x+4)} \div \frac{3(x+2)}{(x+4)(x)}$

---

• 4.
  Convert Expressions to Factored Form, then Divide
  State the non-permissible values for x, then simplify:
  $\frac{3x^2-12x}{x^2-4} \div \frac{2x^3-8x^2}{x^2-x-6}$

---

• 5.
  Fractions Dividing Fractions
  State the non-permissible values for x, then simplify:
  $\frac{ \frac{25x+10}{4x-10}}{\frac{25x^2+10x}{(2x-5)^2}}$

---

• 6.
  Performing Addition First, then Division
  Simplify:
  $\frac{\frac{3}{2a+6}+\frac{4}{4a-4}}{\frac{3}{a}+5}$

---