Answer
$$x\cdot2-5x+6x\cdot2-8x+\frac{15}{x}x\cdot2-12x+36=-11x+66$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}x\cdot2-5x+6x\cdot2-8x+\frac{15}{x}x\cdot2-12x+36& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}2x-5x+12x-8x+\frac{15}{x}x\cdot2-12x+36 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x+\frac{15}{x}x\cdot2-12x+36 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x+15\cdot2-12x+36 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x+30-12x+36 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}-11x+66\end{aligned} $$ | |
| ① | $$ 6 x \cdot 2 = 12 x $$ |
| ② | Combine like terms: $$ \color{blue}{2x} \color{red}{-5x} + \color{green}{12x} \color{green}{-8x} = \color{green}{x} $$ |
| ③ | Multiply $ \dfrac{15}{x} $ by $ x $ to get $ 15$. Step 1: Write $ x $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Cancel $ \color{red}{ x } $ in first and second fraction. Step 3: Multiply numerators and denominators. $$ \begin{aligned} \frac{15}{x} \cdot x & \xlongequal{\text{Step 1}} \frac{15}{x} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{15}{\color{red}{1}} \cdot \frac{\color{red}{1}}{1} = \\[1ex] &= \frac{15}{1} =15 \end{aligned} $$ |
| ④ | $ 15 \cdot 2 = 30 $ |
| ⑤ | Combine like terms: $$ \color{blue}{x} + \color{red}{30} \color{blue}{-12x} + \color{red}{36} = \color{blue}{-11x} + \color{red}{66} $$ |
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