Make T the subject of the equation \(\frac{av}{1 - v}\) = \(\sqrt{\frac{2v + T}{a + 2T}}\)

A.

T = \(\frac{3av}{1 - v}\)

B.

T = \(\frac{1 + v}{2a^2v^3}\)

C.

T = \(\frac{2v(1 - v)^3 - a^4v^3}{2a^3v^3 + (1 - v)^2}\)

D.

\(\frac{2v(1 - v)^3 - a^4 v^3}{2a^3v^ 3 - (1 - v)^3}\)

Correct answer is D

\(\frac{av}{1 - v}\) = \(\sqrt{\frac{2v + T}{a + 2T}}\)

\(\frac{(av)^3}{(1 - v)^3}\) = \(\frac{2v + T}{a + 2T}\)

\(\frac{a^3v^3}{(1^3 - v)^3}\) = \(\frac{2v + T}{a + 2T}\)

= \(\frac{2v(1 - v)^3 - a^4 v^3}{2a^3v^ 3 - (1 - v)^3}\)