$$\dfrac{10}{7}x-\dfrac{12}{4}x^2=\dfrac{-21x^2+10x}{7}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{10}{7}x-\frac{12}{4}x^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{10x}{7} - \frac{ 12 : \color{orangered}{ 4 } }{ 4 : \color{orangered}{ 4 }} \cdot x^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{10x}{7}-\frac{3}{1}x^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}\frac{10x}{7}-3x^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}\frac{-21x^2+10x}{7}\end{aligned} $$ | |
| ① | Multiply $ \dfrac{10}{7} $ by $ x $ to get $ \dfrac{ 10x }{ 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. $$ \begin{aligned} \frac{10}{7} \cdot x & \xlongequal{\text{Step 1}} \frac{10}{7} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 10 \cdot x }{ 7 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 10x }{ 7 } \end{aligned} $$ |
| ② | Divide both the top and bottom numbers by $ \color{orangered}{ 4 } $. |
| ③ | Multiply $ \dfrac{10}{7} $ by $ x $ to get $ \dfrac{ 10x }{ 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. $$ \begin{aligned} \frac{10}{7} \cdot x & \xlongequal{\text{Step 1}} \frac{10}{7} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 10 \cdot x }{ 7 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 10x }{ 7 } \end{aligned} $$ |
| ④ | Multiply $ \dfrac{10}{7} $ by $ x $ to get $ \dfrac{ 10x }{ 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. $$ \begin{aligned} \frac{10}{7} \cdot x & \xlongequal{\text{Step 1}} \frac{10}{7} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 10 \cdot x }{ 7 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 10x }{ 7 } \end{aligned} $$ |
| ⑤ | Remove 1 from denominator. |
| ⑥ | Subtract $3x^2$ from $ \dfrac{10x}{7} $ to get $ \dfrac{ \color{purple}{ -21x^2+10x } }{ 7 }$. Step 1: Write $ 3x^2 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: To subtract raitonal expressions, both fractions must have the same denominator. |