Question

R = r`sqrt((A+B)/(A-B))`. Make A the subject of the formula?

Answer 1

`A=(B(R^2+r^2))/(R^2-r^2)`

Explanation:

`"to gain access to the contents of the square root"`

`"we require to "color(blue)"square both sides"`

`"Note " sqrtaxxsqrta=a`

`rArr(sqrta)^2=a` that is squaring the square root obtains the value inside the square root.

`rArrR^2=(r^2(A+B))/(A-B)larrcolor(blue)" cross-multiply"`

`rArrR^2(A-B)=r^2(A+B)`

`"we require to isolate the terms with A"`

`"distribute and rearrange"`

`R^2A-R^2B=r^2A+r^2B`

`rArrR^2A-r^2A=r^2B+R^2B`

`"take out A as a common factor, B if we wish"`

`rArrA(R^2-r^2)=B(r^2+R^2)`

`"divide both sides by " (R^2-r^2)`

`rArrA=(B(r^2+R^2))/(R^2-r^2)`