Answer
$$\frac{x^2-8x+15}{15x}\cdot\frac{25}{x^2+5x}=\frac{5x^2-40x+75}{3x^3+15x^2}$$
Explanation
| $$ \begin{aligned}\frac{x^2-8x+15}{15x}\cdot\frac{25}{x^2+5x}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{25x^2-200x+375}{15x^3+75x^2} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{5x^2-40x+75}{3x^3+15x^2}\end{aligned} $$ | |
| ① | Multiply $ \dfrac{x^2-8x+15}{15x} $ by $ \dfrac{25}{x^2+5x} $ to get $ \dfrac{ 25x^2-200x+375 }{ 15x^3+75x^2 } $. Step 1: Multiply numerators and denominators. Step 2: Simplify numerator and denominator. $$ \begin{aligned} \frac{x^2-8x+15}{15x} \cdot \frac{25}{x^2+5x} & \xlongequal{\text{Step 1}} \frac{ \left( x^2-8x+15 \right) \cdot 25 }{ 15x \cdot \left( x^2+5x \right) } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ 25x^2-200x+375 }{ 15x^3+75x^2 } \end{aligned} $$ |
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