Question
Answer
$$\dfrac{\dfrac{7}{x^2+4}}{x\dfrac{y}{x+2}}=\dfrac{7x+14}{x^3y+4xy}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\frac{7}{x^2+4}}{x\frac{y}{x+2}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\frac{7}{x^2+4}}{\frac{xy}{x+2}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{7x+14}{x^3y+4xy}\end{aligned} $$ | |
| ① | Multiply $x$ by $ \dfrac{y}{x+2} $ to get $ \dfrac{ xy }{ x+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. $$ \begin{aligned} x \cdot \frac{y}{x+2} & \xlongequal{\text{Step 1}} \frac{x}{\color{red}{1}} \cdot \frac{y}{x+2} \xlongequal{\text{Step 2}} \frac{ x \cdot y }{ 1 \cdot \left( x+2 \right) } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ xy }{ x+2 } \end{aligned} $$ |
| ② | Divide $ \dfrac{7}{x^2+4} $ by $ \dfrac{xy}{x+2} $ to get $ \dfrac{ 7x+14 }{ x^3y+4xy } $. Step 1: To divide rational expressions, multiply the first fraction by the reciprocal of the second fraction. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{ \frac{7}{x^2+4} }{ \frac{\color{blue}{xy}}{\color{blue}{x+2}} } & \xlongequal{\text{Step 1}} \frac{7}{x^2+4} \cdot \frac{\color{blue}{x+2}}{\color{blue}{xy}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ 7 \cdot \left( x+2 \right) }{ \left( x^2+4 \right) \cdot xy } \xlongequal{\text{Step 3}} \frac{ 7x+14 }{ x^3y+4xy } \end{aligned} $$ |
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Simplify Rational Expressions