Question
Answer
$$\dfrac{8t^2+66t+70}{(3-0.2t+0.1t^2)(t+7)}=\dfrac{8t+10}{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{8t^2+66t+70}{(3-0.2t+0.1t^2)(t+7)}& \xlongequal{ }\frac{8t^2+66t+70}{(3-0t+0.1t^2)(t+7)} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{8t^2+66t+70}{(3-0t+0t^2)(t+7)} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{8t^2+66t+70}{3t+21+0t^2+0t+0t^3+0t^2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{8t^2+66t+70}{3t+21} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{8t+10}{3}\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{30t0t^2}\right) $ by each term in $ \left( t+7\right) $. $$ \left( \color{blue}{30t0t^2}\right) \cdot \left( t+7\right) = 3t+21 \cancel{0t^2}0t0t^3 \cancel{0t^2} $$ |
| ② | Simplify denominator $$ \color{blue}{3t} +21 \, \color{red}{ \cancel{0t^2}} \, \color{blue}{0t} 0t^3 \, \color{red}{ \cancel{0t^2}} \, = \color{blue}{3t} +21 $$ |
| ③ | Simplify $ \dfrac{8t^2+66t+70}{3t+21} $ to $ \dfrac{8t+10}{3} $. Factor both the denominator and the numerator, then cancel the common factor. $\color{blue}{t+7}$. $$ \begin{aligned} \frac{8t^2+66t+70}{3t+21} & =\frac{ \left( 8t+10 \right) \cdot \color{blue}{ \left( t+7 \right) }}{ 3 \cdot \color{blue}{ \left( t+7 \right) }} = \\[1ex] &= \frac{8t+10}{3} \end{aligned} $$ |
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