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Question

Answer

$$x^2-12x+\dfrac{20}{8}x^2-56x=\dfrac{7x^2-136x}{2}$$

Explanation

Tap the blue circles to see an explanation.

$$ \begin{aligned}x^2-12x+\frac{20}{8}x^2-56x& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}x^2-12x + \frac{ 20 : \color{orangered}{ 4 } }{ 8 : \color{orangered}{ 4 }} \cdot x^2 - 56x \xlongequal{ } \\[1 em] & \xlongequal{ }x^2-12x+\frac{5}{2}x^2-56x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^2-12x+\frac{5x^2}{2}-56x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{7x^2-24x}{2}-56x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{7x^2-136x}{2}\end{aligned} $$
①
Divide both the top and bottom numbers by $ \color{orangered}{ 4 } $.
②

Multiply $ \dfrac{5}{2} $ by $ x^2 $ to get $ \dfrac{ 5x^2 }{ 2 } $.

Step 1: Write $ x^2 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{5}{2} \cdot x^2 & \xlongequal{\text{Step 1}} \frac{5}{2} \cdot \frac{x^2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 5 \cdot x^2 }{ 2 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 5x^2 }{ 2 } \end{aligned} $$
③

Add $x^2-12x$ and $ \dfrac{5x^2}{2} $ to get $ \dfrac{ \color{purple}{ 7x^2-24x } }{ 2 }$.

Step 1: Write $ x^2-12x $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

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

$$ \begin{aligned} x^2-12x+ \frac{5x^2}{2} & \xlongequal{\text{Step 1}} \frac{x^2-12x}{\color{red}{1}} + \frac{5x^2}{2} = \frac{ \left( x^2-12x \right) \cdot \color{blue}{ 2 }}{ 1 \cdot \color{blue}{ 2 }} + \frac{ 5x^2 }{ 2 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 2x^2-24x } }{ 2 } + \frac{ \color{purple}{ 5x^2 } }{ 2 }=\frac{ \color{purple}{ 7x^2-24x } }{ 2 } \end{aligned} $$
④

Subtract $56x$ from $ \dfrac{7x^2-24x}{2} $ to get $ \dfrac{ \color{purple}{ 7x^2-136x } }{ 2 }$.

Step 1: Write $ 56x $ 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 $\color{blue}{2}$.

$$ \begin{aligned} \frac{7x^2-24x}{2} -56x & \xlongequal{\text{Step 1}} \frac{7x^2-24x}{2} - \frac{56x}{\color{red}{1}} = \frac{ 7x^2-24x }{ 2 } - \frac{ 56x \cdot \color{blue}{ 2 }}{ 1 \cdot \color{blue}{ 2 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 7x^2-24x } }{ 2 } - \frac{ \color{purple}{ 112x } }{ 2 }=\frac{ \color{purple}{ 7x^2-136x } }{ 2 } \end{aligned} $$
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