Multiply $ \dfrac{x^2+2x+1}{10} $ by $ x^3 $ to get $ \dfrac{ x^5+2x^4+x^3 }{ 10 } $.

Step 1: Write $ x^3 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{x^2+2x+1}{10} \cdot x^3 & \xlongequal{\text{Step 1}} \frac{x^2+2x+1}{10} \cdot \frac{x^3}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( x^2+2x+1 \right) \cdot x^3 }{ 10 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ x^5+2x^4+x^3 }{ 10 } \end{aligned} $$

Divide $ \dfrac{x^5+2x^4+x^3}{10} $ by $ 3-x $ to get $ \dfrac{x^5+2x^4+x^3}{-10x+30} $.

Step 1: To divide rational expressions, multiply the first fraction by the reciprocal of the second fraction.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{ \frac{x^5+2x^4+x^3}{10} }{3-x} & \xlongequal{\text{Step 1}} \frac{x^5+2x^4+x^3}{10} \cdot \frac{\color{blue}{1}}{\color{blue}{3-x}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \left( x^5+2x^4+x^3 \right) \cdot 1 }{ 10 \cdot \left( 3-x \right) } \xlongequal{\text{Step 3}} \frac{ x^5+2x^4+x^3 }{ 30-10x } = \\[1ex] &= \frac{x^5+2x^4+x^3}{-10x+30} \end{aligned} $$

Divide $ \dfrac{x^5+2x^4+x^3}{-10x+30} $ by $ 5 $ to get $ \dfrac{ x^5+2x^4+x^3 }{ -50x+150 } $.

Step 1: To divide rational expressions, multiply the first fraction by the reciprocal of the second fraction.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{ \frac{x^5+2x^4+x^3}{-10x+30} }{5} & \xlongequal{\text{Step 1}} \frac{x^5+2x^4+x^3}{-10x+30} \cdot \frac{\color{blue}{1}}{\color{blue}{5}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \left( x^5+2x^4+x^3 \right) \cdot 1 }{ \left( -10x+30 \right) \cdot 5 } \xlongequal{\text{Step 3}} \frac{ x^5+2x^4+x^3 }{ -50x+150 } \end{aligned} $$