Given that \( D=\frac{\sqrt{F+P}}{F-P} \), make \( P \) the Subject

of the EquationTo make \( P \) the subject of the equation, we need to isolate \( P \) on one side of the equation. Here's how we can do it step by step: Given equation: \[ D = \frac{\sqrt{F + P}}{F - P} \] Step 1: Multiply both sides by \( F - P \) to eliminate the denominator: \[ D(F - P) = \sqrt{F + P} \] Step 2: Square both sides to eliminate the square root: \[ [D(F - P)]^2 = (\sqrt{F + P})^2 \] \[ D^2(F - P)^2 = F + P \] Step 3: Expand the left side of the equation: \[ D^2(F^2 - 2FP + P^2) = F + P \] Step 4: Move all terms involving \( P \) to one side and the rest to the other side: \[ D^2P^2 - 2D^2FP + D^2F^2 - F - P = 0 \] Step 5: Move the constant term to the other side: \[ D^2P^2 - 2D^2FP + D^2F^2 - F = P \] Step 6: Move the \( P \) term to the other side: \[ D^2P^2 - 2D^2FP + D^2F^2 - F - P = 0 \] Step 7: Factor out \( P \) from the terms involving \( P \): \[ P(D^2P - 2D^2F - 1) = F - D^2F^2 \] Step 8: Divide both sides by the coefficient of \( P \) to isolate \( P \): \[ P = \frac{F - D^2F^2}{D^2P - 2D^2F - 1} \] This is the equation with \( P \) isolated. Note that the denominator \( D^2P - 2D^2F - 1 \) must not be zero, as division by zero is undefined.