Tap the blue circles to see an explanation.
$$ \begin{aligned}3 \cdot \frac{x}{5}+\frac{x-5}{2}x& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{3x}{5}+\frac{x^2-5x}{2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{5x^2-19x}{10}\end{aligned} $$ | |
① | Step 1: Write $ 3 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 3 \cdot \frac{x}{5} & \xlongequal{\text{Step 1}} \frac{3}{\color{red}{1}} \cdot \frac{x}{5} \xlongequal{\text{Step 2}} \frac{ 3 \cdot x }{ 1 \cdot 5 } \xlongequal{\text{Step 3}} \frac{ 3x }{ 5 } \end{aligned} $$ |
② | 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. $$ \begin{aligned} \frac{x-5}{2} \cdot x & \xlongequal{\text{Step 1}} \frac{x-5}{2} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( x-5 \right) \cdot x }{ 2 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ x^2-5x }{ 2 } \end{aligned} $$ |
③ | To add raitonal expressions, both fractions must have the same denominator. |