Question

How to make b the subject of the formula?

`a=sqrt((3b+c)/(b-c)`

Answer 1

`color(blue)(b) = (c+a^2c)/((a^2-3))`

Explanation:

The first problem you should notice is that there are two terms in `b`. We need to get them both on one side of the equation.

Get rid of the square root first by squaring both sides.

`a^2 = (3b+c)/(b-c)`

`a^2(b-c) = 3b+c" "larr` multiply out the bracket

`color(blue)(a^2b) -a^2c =color(blue)(3b)+c`

`color(blue)(a^2b-3b)= c +a^2c" "larr` both `b` terms on one side

`color(blue)(b)(a^2 -3) = c+a^2c" "` factor out the common factor `b`
`color(blue)(b) = (c+a^2c)/((a^2-3))`