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

1 Answer
Jim G.
Jun 28, 2017

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)

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