Make \( g \) the subject of \( e=\sqrt{\frac{7 g+5}{11+2 g}} \)

To make \( g \) the subject of the equation \( e=\sqrt{\frac{7 g+5}{11+2 g}} \), we start by squaring both sides to eliminate the square root: \[ e^2 = \frac{7g + 5}{11 + 2g} \] Next, we can cross-multiply to eliminate the fraction: \[ e^2(11 + 2g) = 7g + 5 \] Expanding the left side gives: \[ 11e^2 + 2ge^2 = 7g + 5 \] Now, we need to rearrange the equation to isolate \( g \). Let's move all terms involving \( g \) to one side and constant terms to the other: \[ 2ge^2 - 7g = 5 - 11e^2 \] Factoring \( g \) out from the left side gives: \[ g(2e^2 - 7) = 5 - 11e^2 \] Now, we can solve for \( g \) by dividing both sides by \( 2e^2 - 7 \): \[ g = \frac{5 - 11e^2}{2e^2 - 7} \] And that's our final expression with \( g \) as the subject!