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Answer

$$x\cdot3-2x\cdot2-25x+\frac{50}{x}\cdot2-25=\frac{-26x^2-25x+100}{x}$$

Explanation

Tap the blue circles to see an explanation.

$$ \begin{aligned}x\cdot3-2x\cdot2-25x+\frac{50}{x}\cdot2-25& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}3x-4x-25x+\frac{50}{x}\cdot2-25 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-26x+\frac{50}{x}\cdot2-25 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-26x+\frac{100}{x}-25 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{-26x^2+100}{x}-25 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}\frac{-26x^2-25x+100}{x}\end{aligned} $$
①
$$ 2 x \cdot 2 = 4 x $$
②

Combine like terms:

$$ \color{blue}{3x} \color{red}{-4x} \color{red}{-25x} = \color{red}{-26x} $$
③

Multiply $ \dfrac{50}{x} $ by $ 2 $ to get $ \dfrac{ 100 }{ x } $.

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.

$$ \begin{aligned} \frac{50}{x} \cdot 2 & \xlongequal{\text{Step 1}} \frac{50}{x} \cdot \frac{2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 50 \cdot 2 }{ x \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 100 }{ x } \end{aligned} $$
④

Add $-26x$ and $ \dfrac{100}{x} $ to get $ \dfrac{ \color{purple}{ -26x^2+100 } }{ x }$.

Step 1: Write $ -26x $ 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 $\color{blue}{ x }$.

$$ \begin{aligned} -26x+ \frac{100}{x} & \xlongequal{\text{Step 1}} \frac{-26x}{\color{red}{1}} + \frac{100}{x} = \frac{ \left( -26x \right) \cdot \color{blue}{ x }}{ 1 \cdot \color{blue}{ x }} + \frac{ 100 }{ x } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ -26x^2 } }{ x } + \frac{ \color{purple}{ 100 } }{ x }=\frac{ \color{purple}{ -26x^2+100 } }{ x } \end{aligned} $$
⑤

Subtract $25$ from $ \dfrac{-26x^2+100}{x} $ to get $ \dfrac{ \color{purple}{ -26x^2-25x+100 } }{ x }$.

Step 1: Write $ 25 $ 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 $\color{blue}{x}$.

$$ \begin{aligned} \frac{-26x^2+100}{x} -25 & \xlongequal{\text{Step 1}} \frac{-26x^2+100}{x} - \frac{25}{\color{red}{1}} = \frac{ -26x^2+100 }{ x } - \frac{ 25 \cdot \color{blue}{ x }}{ 1 \cdot \color{blue}{ x }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ -26x^2+100 } }{ x } - \frac{ \color{purple}{ 25x } }{ x }=\frac{ \color{purple}{ -26x^2-25x+100 } }{ x } \end{aligned} $$
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