Multiplying rational expressions

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  1. Review: Multiplying Monomials
  1. Simplifying Rational Expressions Involving Multiplication
    State the non-permissible values, then simplify:
    5x2y3x2y2×9z3x4y215y3z2\frac{5x^2y^3}{x^2y^2} \times \frac{9z^3x^4y^2}{15y^3z^2}
    1. Multiplying Rational Expressions in Factored Form
      State the non-permissible values, then simplify:
      (x+2)(x12)(x+4)×2(x+4)x(x+2)\frac{(x+2)}{(x-12)(x+4)} \times \frac{2(x+4)}{x(x+2)}
      1. Convert Expressions to Factored Form, then multiply
        State the non-permissible values, then simplify:
        1. 5x215x30x210x×3x2+8x3(x29) \frac{5x^2-15x}{30x^2-10x} \times \frac{3x^2+8x-3}{(x^2-9)}
        2. 5x+208x4×10x5(4+x)2 \frac{5x+20}{8x-4} \times \frac{10x-5}{(4+x)^2}
        3. (x2+9x+8)(49x3x)(7x2+55x8)(x2+x) \frac{(x^2+9x+8)(49x^3-x)}{(7x^2+55x-8)(x^2+x)}
      Topic Notes
      \bullet multiplication rule: xaxb=xa+bx^a \cdot x^b=x^{a+b}
      \bullet division rule: xaxb=xab\frac{x^a}{x^b}=x^{a-b}