Multiply $25$ by $ \dfrac{x}{4} $ to get $ \dfrac{ 25x }{ 4 } $.

Step 1: Write $ 25 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 25 \cdot \frac{x}{4} & \xlongequal{\text{Step 1}} \frac{25}{\color{red}{1}} \cdot \frac{x}{4} \xlongequal{\text{Step 2}} \frac{ 25 \cdot x }{ 1 \cdot 4 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 25x }{ 4 } \end{aligned} $$

Multiply $5$ by $ \dfrac{x}{7} $ to get $ \dfrac{ 5x }{ 7 } $.

Step 1: Write $ 5 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 5 \cdot \frac{x}{7} & \xlongequal{\text{Step 1}} \frac{5}{\color{red}{1}} \cdot \frac{x}{7} \xlongequal{\text{Step 2}} \frac{ 5 \cdot x }{ 1 \cdot 7 } \xlongequal{\text{Step 3}} \frac{ 5x }{ 7 } \end{aligned} $$

Multiply $ \dfrac{25x}{4} $ by $ x^2 $ to get $ \dfrac{ 25x^3 }{ 4 } $.

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.

$$ \begin{aligned} \frac{25x}{4} \cdot x^2 & \xlongequal{\text{Step 1}} \frac{25x}{4} \cdot \frac{x^2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 25x \cdot x^2 }{ 4 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 25x^3 }{ 4 } \end{aligned} $$

Multiply $ \dfrac{5x}{7} $ by $ x $ to get $ \dfrac{ 5x^2 }{ 7 } $.

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.

$$ \begin{aligned} \frac{5x}{7} \cdot x & \xlongequal{\text{Step 1}} \frac{5x}{7} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 5x \cdot x }{ 7 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 5x^2 }{ 7 } \end{aligned} $$

Multiply $ \dfrac{25x^3}{4} $ by $ 2 $ to get $ \dfrac{ 50x^3 }{ 4 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{25x^3}{4} \cdot 2 & \xlongequal{\text{Step 1}} \frac{25x^3}{4} \cdot \frac{2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 25x^3 \cdot 2 }{ 4 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 50x^3 }{ 4 } \end{aligned} $$

Multiply $ \dfrac{5x}{7} $ by $ x $ to get $ \dfrac{ 5x^2 }{ 7 } $.

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.

$$ \begin{aligned} \frac{5x}{7} \cdot x & \xlongequal{\text{Step 1}} \frac{5x}{7} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 5x \cdot x }{ 7 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 5x^2 }{ 7 } \end{aligned} $$

Multiply $ \dfrac{50x^3}{4} $ by $ x^2 $ to get $ \dfrac{ 50x^5 }{ 4 } $.

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.

$$ \begin{aligned} \frac{50x^3}{4} \cdot x^2 & \xlongequal{\text{Step 1}} \frac{50x^3}{4} \cdot \frac{x^2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 50x^3 \cdot x^2 }{ 4 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 50x^5 }{ 4 } \end{aligned} $$

Multiply $ \dfrac{5x}{7} $ by $ x $ to get $ \dfrac{ 5x^2 }{ 7 } $.

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.

$$ \begin{aligned} \frac{5x}{7} \cdot x & \xlongequal{\text{Step 1}} \frac{5x}{7} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 5x \cdot x }{ 7 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 5x^2 }{ 7 } \end{aligned} $$

Subtract $ \dfrac{50x^5}{4} $ from $ x^3 $ to get $ \dfrac{ \color{purple}{ -50x^5+4x^3 } }{ 4 }$.

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

Step 2: To subtract raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ 4 }$.

$$ \begin{aligned} x^3- \frac{50x^5}{4} & \xlongequal{\text{Step 1}} \frac{x^3}{\color{red}{1}} - \frac{50x^5}{4} = \frac{ x^3 \cdot \color{blue}{ 4 }}{ 1 \cdot \color{blue}{ 4 }} - \frac{ 50x^5 }{ 4 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 4x^3 } }{ 4 } - \frac{ \color{purple}{ 50x^5 } }{ 4 }=\frac{ \color{purple}{ -50x^5+4x^3 } }{ 4 } \end{aligned} $$

Multiply $ \dfrac{5x}{7} $ by $ x $ to get $ \dfrac{ 5x^2 }{ 7 } $.

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.

$$ \begin{aligned} \frac{5x}{7} \cdot x & \xlongequal{\text{Step 1}} \frac{5x}{7} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 5x \cdot x }{ 7 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 5x^2 }{ 7 } \end{aligned} $$

Subtract $ \dfrac{2}{x^2} $ from $ \dfrac{-50x^5+4x^3}{4} $ to get $ \dfrac{ \color{purple}{ -50x^7+4x^5-8 } }{ 4x^2 }$.

To subtract raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $ \color{blue}{ x^2 }$ and the second by $\color{blue}{ 4 }$.

$$ \begin{aligned} \frac{-50x^5+4x^3}{4} - \frac{2}{x^2} & = \frac{ \left( -50x^5+4x^3 \right) \cdot \color{blue}{ x^2 }}{ 4 \cdot \color{blue}{ x^2 }} - \frac{ 2 \cdot \color{blue}{ 4 }}{ x^2 \cdot \color{blue}{ 4 }} = \\[1ex] &=\frac{ \color{purple}{ -50x^7+4x^5 } }{ 4x^2 } - \frac{ \color{purple}{ 8 } }{ 4x^2 }=\frac{ \color{purple}{ -50x^7+4x^5-8 } }{ 4x^2 } \end{aligned} $$

Multiply $ \dfrac{5x}{7} $ by $ x $ to get $ \dfrac{ 5x^2 }{ 7 } $.

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.

$$ \begin{aligned} \frac{5x}{7} \cdot x & \xlongequal{\text{Step 1}} \frac{5x}{7} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 5x \cdot x }{ 7 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 5x^2 }{ 7 } \end{aligned} $$

Subtract $6x$ from $ \dfrac{-50x^7+4x^5-8}{4x^2} $ to get $ \dfrac{ \color{purple}{ -50x^7+4x^5-24x^3-8 } }{ 4x^2 }$.

Step 1: Write $ 6x $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To subtract raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{4x^2}$.

$$ \begin{aligned} \frac{-50x^7+4x^5-8}{4x^2} -6x & \xlongequal{\text{Step 1}} \frac{-50x^7+4x^5-8}{4x^2} - \frac{6x}{\color{red}{1}} = \frac{ -50x^7+4x^5-8 }{ 4x^2 } - \frac{ 6x \cdot \color{blue}{ 4x^2 }}{ 1 \cdot \color{blue}{ 4x^2 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ -50x^7+4x^5-8 } }{ 4x^2 } - \frac{ \color{purple}{ 24x^3 } }{ 4x^2 }=\frac{ \color{purple}{ -50x^7+4x^5-24x^3-8 } }{ 4x^2 } \end{aligned} $$

Multiply $ \dfrac{5x}{7} $ by $ x $ to get $ \dfrac{ 5x^2 }{ 7 } $.

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.

$$ \begin{aligned} \frac{5x}{7} \cdot x & \xlongequal{\text{Step 1}} \frac{5x}{7} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 5x \cdot x }{ 7 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 5x^2 }{ 7 } \end{aligned} $$

Add $ \dfrac{-50x^7+4x^5-24x^3-8}{4x^2} $ and $ \dfrac{5}{x^2} $ to get $ \dfrac{ \color{purple}{ -50x^9+4x^7-24x^5+12x^2 } }{ 4x^4 }$.

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}{ x^2 }$ and the second by $\color{blue}{ 4x^2 }$.

$$ \begin{aligned} \frac{-50x^7+4x^5-24x^3-8}{4x^2} + \frac{5}{x^2} & = \frac{ \left( -50x^7+4x^5-24x^3-8 \right) \cdot \color{blue}{ x^2 }}{ 4x^2 \cdot \color{blue}{ x^2 }} + \frac{ 5 \cdot \color{blue}{ 4x^2 }}{ x^2 \cdot \color{blue}{ 4x^2 }} = \\[1ex] &=\frac{ \color{purple}{ -50x^9+4x^7-24x^5-8x^2 } }{ 4x^4 } + \frac{ \color{purple}{ 20x^2 } }{ 4x^4 }=\frac{ \color{purple}{ -50x^9+4x^7-24x^5+12x^2 } }{ 4x^4 } \end{aligned} $$

Multiply $ \dfrac{5x}{7} $ by $ x $ to get $ \dfrac{ 5x^2 }{ 7 } $.

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.

$$ \begin{aligned} \frac{5x}{7} \cdot x & \xlongequal{\text{Step 1}} \frac{5x}{7} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 5x \cdot x }{ 7 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 5x^2 }{ 7 } \end{aligned} $$

Add $ \dfrac{-50x^9+4x^7-24x^5+12x^2}{4x^4} $ and $ \dfrac{5x^2}{7} $ to get $ \dfrac{ \color{purple}{ -350x^9+28x^7+20x^6-168x^5+84x^2 } }{ 28x^4 }$.

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}{ 7 }$ and the second by $\color{blue}{ 4x^4 }$.

$$ \begin{aligned} \frac{-50x^9+4x^7-24x^5+12x^2}{4x^4} + \frac{5x^2}{7} & = \frac{ \left( -50x^9+4x^7-24x^5+12x^2 \right) \cdot \color{blue}{ 7 }}{ 4x^4 \cdot \color{blue}{ 7 }} + \frac{ 5x^2 \cdot \color{blue}{ 4x^4 }}{ 7 \cdot \color{blue}{ 4x^4 }} = \\[1ex] &=\frac{ \color{purple}{ -350x^9+28x^7-168x^5+84x^2 } }{ 28x^4 } + \frac{ \color{purple}{ 20x^6 } }{ 28x^4 } = \\[1ex] &=\frac{ \color{purple}{ -350x^9+28x^7+20x^6-168x^5+84x^2 } }{ 28x^4 } \end{aligned} $$

Add $ \dfrac{-350x^9+28x^7+20x^6-168x^5+84x^2}{28x^4} $ and $ 7 $ to get $ \dfrac{ \color{purple}{ -350x^9+28x^7+20x^6-168x^5+196x^4+84x^2 } }{ 28x^4 }$.

Step 1: Write $ 7 $ 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 second fraction by $\color{blue}{28x^4}$.

$$ \begin{aligned} \frac{-350x^9+28x^7+20x^6-168x^5+84x^2}{28x^4} +7 & \xlongequal{\text{Step 1}} \frac{-350x^9+28x^7+20x^6-168x^5+84x^2}{28x^4} + \frac{7}{\color{red}{1}} = \\[1ex] &= \frac{ -350x^9+28x^7+20x^6-168x^5+84x^2 }{ 28x^4 } + \frac{ 7 \cdot \color{blue}{ 28x^4 }}{ 1 \cdot \color{blue}{ 28x^4 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ -350x^9+28x^7+20x^6-168x^5+84x^2 } }{ 28x^4 } + \frac{ \color{purple}{ 196x^4 } }{ 28x^4 } = \\[1ex] &=\frac{ \color{purple}{ -350x^9+28x^7+20x^6-168x^5+196x^4+84x^2 } }{ 28x^4 } \end{aligned} $$