Rearranging a formula to make another variable (letter) the subject. In order for a letter to be the subject, it must be isolated on one side of the equals sign e.g. in the formula $y=mx+c$, y is the subject as it is by itself on the left hand side of the equals sign. NB a subject can also be on the right hand side like in $e+fg=h$ where h is the subject.
Example 1 Make b the subject of the formula $$a=b+cd$$ We identify the terms which are on the same side of the equals sign as the subject. Here, we have '$+cd$' which needs to be removed from b. We can do this by subtracting cd from both sides of the equation: $$a-cd=b$$
Example 2 Make m the subject of the formula $$x=\frac{3m+1}{m+3}$$
In this particular case, where the subject is in two separate places, the strategy is always the same. Collect the two 'm' terms on the same side of the equation and then factorise the m out as shown below:
$$x(m+3)=3m+1$$ Here we multiplied both sides of the equation by the denominator
Expand the brackets $$mx + 3x = 3m + 1$$ Collect the subject on one side of the equation and remove anything that doesn't contain 'm' $$mx-3m=1-3x$$
Factorise m out of the two terms and finally divide by the bracket $$m(x-3)=1-3x$$
$$m=\frac{1-3x}{x-3}$$