$$\dfrac{\dfrac{x^2-9x}{2}+10}{\dfrac{x}{8}-\dfrac{x+5}{16}}=\dfrac{16x-64}{2}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\frac{x^2-9x}{2}+10}{\frac{x}{8}-\frac{x+5}{16}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{\frac{x^2-9x+20}{2}}{\frac{x-5}{16}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{16x-64}{2}\end{aligned} $$ | |
| ① | Add $ \dfrac{x^2-9x}{2} $ and $ 10 $ to get $ \dfrac{ \color{purple}{ x^2-9x+20 } }{ 2 }$. Step 1: Write $ 10 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: To add raitonal expressions, both fractions must have the same denominator. |
| ② | Subtract $ \dfrac{x+5}{16} $ from $ \dfrac{x}{8} $ to get $ \dfrac{ \color{purple}{ x-5 } }{ 16 }$. To subtract raitonal expressions, both fractions must have the same denominator. |
| ③ | Divide $ \dfrac{x^2-9x+20}{2} $ by $ \dfrac{x-5}{16} $ to get $ \dfrac{ 16x-64 }{ 2 } $. Step 1: To divide rational expressions, multiply the first fraction by the reciprocal of the second fraction. Step 2: Factor numerators and denominators. Step 3: Cancel common factors. Step 4: Multiply numerators and denominators. Step 5: Simplify numerator and denominator. $$ \begin{aligned} \frac{ \frac{x^2-9x+20}{2} }{ \frac{\color{blue}{x-5}}{\color{blue}{16}} } & \xlongequal{\text{Step 1}} \frac{x^2-9x+20}{2} \cdot \frac{\color{blue}{16}}{\color{blue}{x-5}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \left( x-4 \right) \cdot \color{blue}{ \left( x-5 \right) } }{ 2 } \cdot \frac{ 16 }{ 1 \cdot \color{blue}{ \left( x-5 \right) } } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ x-4 }{ 2 } \cdot \frac{ 16 }{ 1 } \xlongequal{\text{Step 4}} \frac{ \left( x-4 \right) \cdot 16 }{ 2 \cdot 1 } \xlongequal{\text{Step 5}} \frac{ 16x-64 }{ 2 } \end{aligned} $$ |