Solve the formula for the given variable. \[ Z=\frac{9}{f-s} \] Solve for \( f \), then solve for \( s \). \( f=\square \) (Simplify your answer.)
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Beyond the Answer
To solve for \( f \), we start with the equation \( Z=\frac{9}{f-s} \). First, we multiply both sides by \( (f-s) \) to eliminate the fraction: \[ Z(f-s) = 9. \] Now, we can distribute \( Z \): \[ Zf - Zs = 9. \] Next, we want to isolate \( f \): \[ Zf = 9 + Zs. \] Now, dividing by \( Z \): \[ f = \frac{9 + Zs}{Z}. \] Now, to solve for \( s \), we start again from the original formula: \[ Z=\frac{9}{f-s}. \] Multiplying both sides by \( (f-s) \): \[ Z(f-s) = 9. \] Distributing again gives: \[ Zf - Zs = 9. \] Rearranging to isolate \( s \): \[ Zs = Zf - 9. \] Now we divide by \( Z \): \[ s = \frac{Zf - 9}{Z}. \] Thus, we have the solutions as follows: \( f=\frac{9 + Zs}{Z} \) and \( s=\frac{Zf - 9}{Z}. \)
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