\[\begin{array}{rl} (P\div R)(x)=P(x)\div R(x)&\text{Replace }P(x)\text{ and }R(x) \\ (P\div R)(x)=\dfrac{3x^2+14x+8}{3x^2+8x-16}\div\dfrac{3x^2-4x-4}{x^2-3x+2}&\text{Form the reciprocal of }R\text{ a...\[\begin{array}{rl} (P\div R)(x)=P(x)\div R(x)&\text{Replace }P(x)\text{ and }R(x) \\ (P\div R)(x)=\dfrac{3x^2+14x+8}{3x^2+8x-16}\div\dfrac{3x^2-4x-4}{x^2-3x+2}&\text{Form the reciprocal of }R\text{ and write as multiplication} \\ (P\div R)(x)=\dfrac{3x^2+14x+8}{3x^2+8x-16}\cdot\dfrac{x^2-3x+2}{3x^2-4x-4}&\text{Factor each numerator and denominator} \\ (P\div R)(x)=\dfrac{(3x+2)(x+4)}{(3x-4)(x+4)}\cdot\dfrac{(x-2)(x-1)}{(3x+2)(x-2)}&\text{Reduce} \\ (P\div R)(x)=\dfrac{\cancel{(3x+2)}\cancel{(x…
