Answer
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{y^2+8y+7}{3y+9}div\frac{y^2+y}{y^2+5y+6}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{dy^2+8dy+7d}{3y+9}iv\frac{y^2+y}{y^2+5y+6} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{diy^2+8diy+7di}{3y+9}v\frac{y^2+y}{y^2+5y+6} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{divy^2+8divy+7div}{3y+9}\frac{y^2+y}{y^2+5y+6} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{divy^4+9divy^3+15divy^2+7divy}{3y^3+24y^2+63y+54}\end{aligned} $$ | |
| ① | Multiply $ \dfrac{y^2+8y+7}{3y+9} $ by $ d $ to get $ \dfrac{ dy^2+8dy+7d }{ 3y+9 } $. Step 1: Write $ d $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{y^2+8y+7}{3y+9} \cdot d & \xlongequal{\text{Step 1}} \frac{y^2+8y+7}{3y+9} \cdot \frac{d}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( y^2+8y+7 \right) \cdot d }{ \left( 3y+9 \right) \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ dy^2+8dy+7d }{ 3y+9 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{dy^2+8dy+7d}{3y+9} $ by $ i $ to get $ \dfrac{ diy^2+8diy+7di }{ 3y+9 } $. Step 1: Write $ i $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{dy^2+8dy+7d}{3y+9} \cdot i & \xlongequal{\text{Step 1}} \frac{dy^2+8dy+7d}{3y+9} \cdot \frac{i}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( dy^2+8dy+7d \right) \cdot i }{ \left( 3y+9 \right) \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ diy^2+8diy+7di }{ 3y+9 } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{diy^2+8diy+7di}{3y+9} $ by $ v $ to get $ \dfrac{ divy^2+8divy+7div }{ 3y+9 } $. Step 1: Write $ v $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{diy^2+8diy+7di}{3y+9} \cdot v & \xlongequal{\text{Step 1}} \frac{diy^2+8diy+7di}{3y+9} \cdot \frac{v}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( diy^2+8diy+7di \right) \cdot v }{ \left( 3y+9 \right) \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ divy^2+8divy+7div }{ 3y+9 } \end{aligned} $$ |
| ④ | Multiply $ \dfrac{divy^2+8divy+7div}{3y+9} $ by $ \dfrac{y^2+y}{y^2+5y+6} $ to get $ \dfrac{divy^4+9divy^3+15divy^2+7divy}{3y^3+24y^2+63y+54} $. Step 1: Multiply numerators and denominators. Step 2: Simplify numerator and denominator. $$ \begin{aligned} \frac{divy^2+8divy+7div}{3y+9} \cdot \frac{y^2+y}{y^2+5y+6} & \xlongequal{\text{Step 1}} \frac{ \left( divy^2+8divy+7div \right) \cdot \left( y^2+y \right) }{ \left( 3y+9 \right) \cdot \left( y^2+5y+6 \right) } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ divy^4+divy^3+8divy^3+8divy^2+7divy^2+7divy }{ 3y^3+15y^2+18y+9y^2+45y+54 } = \frac{divy^4+9divy^3+15divy^2+7divy}{3y^3+24y^2+63y+54} \end{aligned} $$ |