Multiply $ \color{blue}{-8} $ by $ \left( x+2\right) $ $$ \color{blue}{-8} \cdot \left( x+2\right) = -8x-16 $$Multiply $ \color{blue}{3} $ by $ \left( x+2\right) $ $$ \color{blue}{3} \cdot \left( x+2\right) = 3x+6 $$

Combine like terms:

$$ \color{blue}{15} -8x \color{blue}{-16} = -8x \color{blue}{-1} $$

$$ \left( \color{blue}{3x+6}\right) \cdot x = 3x^2+6x $$

Combine like terms:

$$ \color{blue}{-8x} -1+3x^2+ \color{blue}{6x} = 3x^2 \color{blue}{-2x} -1 $$

Multiply $ \dfrac{-11}{15} $ by $ x+2 $ to get $ \dfrac{ -11x-22 }{ 15 } $.

Step 1: Write $ x+2 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{-11}{15} \cdot x+2 & \xlongequal{\text{Step 1}} \frac{-11}{15} \cdot \frac{x+2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( -11 \right) \cdot \left( x+2 \right) }{ 15 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ -11x-22 }{ 15 } \end{aligned} $$

Multiply $ \dfrac{-11x-22}{15} $ by $ x $ to get $ \dfrac{ -11x^2-22x }{ 15 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{-11x-22}{15} \cdot x & \xlongequal{\text{Step 1}} \frac{-11x-22}{15} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( -11x-22 \right) \cdot x }{ 15 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ -11x^2-22x }{ 15 } \end{aligned} $$

Multiply $ \dfrac{-11x^2-22x}{15} $ by $ x-1 $ to get $ \dfrac{-11x^3-11x^2+22x}{15} $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{-11x^2-22x}{15} \cdot x-1 & \xlongequal{\text{Step 1}} \frac{-11x^2-22x}{15} \cdot \frac{x-1}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( -11x^2-22x \right) \cdot \left( x-1 \right) }{ 15 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ -11x^3+11x^2-22x^2+22x }{ 15 } = \frac{-11x^3-11x^2+22x}{15} \end{aligned} $$

Add $3x^2-2x-1$ and $ \dfrac{-11x^3-11x^2+22x}{15} $ to get $ \dfrac{ \color{purple}{ -11x^3+34x^2-8x-15 } }{ 15 }$.

Step 1: Write $ 3x^2-2x-1 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ 15 }$.

$$ \begin{aligned} 3x^2-2x-1+ \frac{-11x^3-11x^2+22x}{15} & \xlongequal{\text{Step 1}} \frac{3x^2-2x-1}{\color{red}{1}} + \frac{-11x^3-11x^2+22x}{15} = \\[1ex] &= \frac{ \left( 3x^2-2x-1 \right) \cdot \color{blue}{ 15 }}{ 1 \cdot \color{blue}{ 15 }} + \frac{ -11x^3-11x^2+22x }{ 15 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 45x^2-30x-15 } }{ 15 } + \frac{ \color{purple}{ -11x^3-11x^2+22x } }{ 15 }=\frac{ \color{purple}{ -11x^3+34x^2-8x-15 } }{ 15 } \end{aligned} $$