Math Calculators, Lessons and Formulas

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Question

Answer

$$\dfrac{\dfrac{\dfrac{8}{1}+8}{8}}{a}-8=\dfrac{-8a+2}{a}$$

Explanation

Tap the blue circles to see an explanation.

$$ \begin{aligned}\frac{\frac{\frac{8}{1}+8}{8}}{a}-8& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\frac{16}{8}}{a}-8 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{ \frac{ 16 : \color{orangered}{ 8 } }{ 8 : \color{orangered}{ 8 }} }{ a } - 8 \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{\frac{2}{1}}{a}-8 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{2}{a}-8 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{-8a+2}{a}\end{aligned} $$
①
Simplify numerator and denominator
②
Divide both the top and bottom numbers by $ \color{orangered}{ 8 } $.
③
Remove 1 from denominator.
④

Subtract $8$ from $ \dfrac{2}{a} $ to get $ \dfrac{ \color{purple}{ -8a+2 } }{ a }$.

Step 1: Write $ 8 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To subtract raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{a}$.

$$ \begin{aligned} \frac{2}{a} -8 & \xlongequal{\text{Step 1}} \frac{2}{a} - \frac{8}{\color{red}{1}} = \frac{ 2 }{ a } - \frac{ 8 \cdot \color{blue}{ a }}{ 1 \cdot \color{blue}{ a }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 2 } }{ a } - \frac{ \color{purple}{ 8a } }{ a }=\frac{ \color{purple}{ -8a+2 } }{ a } \end{aligned} $$
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Simplify Rational Expressions