Question
Answer
$$x^2-7x+\dfrac{12}{2}x^2-9x+9=7x^2-16x+9$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}x^2-7x+\frac{12}{2}x^2-9x+9& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}x^2-7x + \frac{ 12 : \color{orangered}{ 2 } }{ 2 : \color{orangered}{ 2 }} \cdot x^2 - 9x + 9 \xlongequal{ } \\[1 em] & \xlongequal{ }x^2-7x+\frac{6}{1}x^2-9x+9 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^2-7x+6x^2-9x+9 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}7x^2-7x-9x+9 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}7x^2-16x+9\end{aligned} $$ | |
| ① | Divide both the top and bottom numbers by $ \color{orangered}{ 2 } $. |
| ② | Remove 1 from denominator. |
| ③ | Combine like terms: $$ \color{blue}{x^2} -7x+ \color{blue}{6x^2} = \color{blue}{7x^2} -7x $$ |
| ④ | Combine like terms: $$ 7x^2 \color{blue}{-7x} \color{blue}{-9x} +9 = 7x^2 \color{blue}{-16x} +9 $$ |
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