Question
Answer
$$\dfrac{(-5+x)^2-25}{x}=\dfrac{x^2-10x}{x}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{(-5+x)^2-25}{x}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{25-10x+x^2-25}{x} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{x^2-10x}{x}\end{aligned} $$ | |
| ① | Find $ \left(-5+x\right)^2 $ in two steps. S1: Change all signs inside bracket. S2: Apply formula $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 5 } $ and $ B = \color{red}{ x }$. $$ \begin{aligned}\left(-5+x\right)^2& \xlongequal{ S1 } \left(5-x\right)^2 \xlongequal{ S2 } \color{blue}{5^2} -2 \cdot 5 \cdot x + \color{red}{x^2} = \\[1 em] & = 25-10x+x^2\end{aligned} $$ |
| ② | Simplify numerator $$ \, \color{blue}{ \cancel{25}} \,-10x+x^2 \, \color{blue}{ -\cancel{25}} \, = x^2-10x $$ |
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