Rearranging Equations – When the Term you Want is Being Subtracted From

Sometimes we are stuck with a term that is being subtracted from. Just like a numerator, it is being done to rather than doing, so it doesn’t have an inverse operation. There is a way around this; let’s find out what it is.

This is a tricky one. We need to isolate s :

v squared space equals space u squared space minus 2 g s

As it stands, we can’t move u squared because it’s the subject of the subtraction. Therefore we need to change the way that side of the equation is written. In fact, u squared space minus 2 g s is the same as negative 2 g s space plus space u squared (check using a calculator if you don’t believe it). So we can rewrite the equation as:

v squared space equals space minus 2 g s space plus space space u squared

That makes our job easier. We can now subtract from both sides giving us:

v squared space minus space u squared space equals space minus 2 g s space space

And now divide both sides by negative 2 g to get:

fraction numerator v squared space minus space u squared over denominator negative 2 g end fraction space equals space s

Generally speaking, to have a negative denominator in an equation is seen as a bad thing because it is an improper fraction. To correct this, we multiply the top and the bottom of this by -1. negative 2 g multiplied by -1 is 2 g comma space v squared multiplied by -1 is -v2 and -u2  multiplied by -1 is u2 so we end up with:

s space equals space fraction numerator u squared space minus space v squared over denominator 2 g end fraction

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