Changing the subject of a formula

The subject is isolated on one side and does not also occur on the other. Undo operations in reverse order, applying the same operation to both sides. If the required letter appears more than once, collect its terms and factorise.

Example

From \(P=2l+2w\), \(\begin{aligned}2w&=P-2l\\w&=\dfrac{P-2l}{2}.\end{aligned}\) If \(P=30\) cm and \(l=9\) cm, then \(w=6\) cm.

Make \(x\) the subject of \(y=\dfrac{x+2}{x-1}\): \(\begin{aligned}y(x-1)&=x+2\\yx-x&=y+2\\x(y-1)&=y+2\\x&=\dfrac{y+2}{y-1},\qquad y\ne1.\end{aligned}\)

When taking a square root, use the context: \(A=\pi r^2\) gives \(r=\sqrt{\dfrac A\pi}\) for a radius, because \(r\ge0\). A length cannot be chosen negative.