Question
Answer
$$\dfrac{x^2+5x+6}{x^2-4x}\cdot4x=\dfrac{4x^2+20x+24}{x-4}$$
Explanation
| $$ \begin{aligned}\frac{x^2+5x+6}{x^2-4x}\cdot4x& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{4x^3+20x^2+24x}{x^2-4x} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{4x^2+20x+24}{x-4}\end{aligned} $$ | |
| ① | Multiply $ \dfrac{x^2+5x+6}{x^2-4x} $ by $ 4x $ to get $ \dfrac{ 4x^3+20x^2+24x }{ x^2-4x } $. Step 1: Write $ 4x $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{x^2+5x+6}{x^2-4x} \cdot 4x & \xlongequal{\text{Step 1}} \frac{x^2+5x+6}{x^2-4x} \cdot \frac{4x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( x^2+5x+6 \right) \cdot 4x }{ \left( x^2-4x \right) \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 4x^3+20x^2+24x }{ x^2-4x } \end{aligned} $$ |
This page was created using
Simplify Rational Expressions