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Skill 8 of 15
In Progress

Rules of algebra

Let’s rearrange some more:

\begin{align} s_y&=v_{y,0}\left(\frac{s_x}{v_{x,0}}\right)-\frac12 g \left(\frac{s_x}{v_{x,0}}\right)^2\\ &=\boldsymbol{\frac{ v_{y,0} s_x}{v_{x,0}}}-\frac12 g \left(\frac{s_x}{v_{x,0}}\right)^2 \\ &= \frac{ v_{y,0} s_x}{v_{x,0}} -\frac12 g \boldsymbol{\frac{s_x^2}{v_{x,0}^2}} \end{align}

Here, in the first step, we moved $v_{y,0}$ into the bracket and to the top (numerator) of the fraction. Because, the numerator counts how many there are of the fraction, and multiplying it with a number does the same thing. It seems to be a general rule, which we could write as:

$$a\left(\frac bc\right)=\frac{ab}c$$

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