Make {p} the subject of the formula D/d=f + p/f - p?

As written D/d = f + p/f − p
subtract f from both sides
∴ D/d − f = p/f − p
factor out the common factor of p
∴ D/d − f = p(1/f − 1)
divide both sides by (1/f − 1)
∴ p = (D/d − f)/((1/f − 1)
∴ p = (D/d − df/d)/(1/f − f/f)
∴ p = [f(D − df)]/[d(1 − f)]

assuming you mean D/d = (f + p)/(f − p)
multiply both sides by (f − p)
∴ D(f − p)/d = f + p
expand the parentheses
∴ Df/d − Dp/d = f + p
add Dp/d to both sides
∴ Df/d = f + p + Dp/d
subtract f from both sides
∴ Df/d − f = p + Dp/d
factor the commen factors
∴ f(D/d − 1) = p(1 + D/d)
divide both sides by (1 + D/d)
∴ p = f(D/d − 1)/(1 + D/d)
∴ p = f(D/d − d/d)/(d/d + D/d)
∴ p = [df(D − d)]/[d(d + D)]
∴ p = f(D − d)/(d + D) ; d ≠ 0

D/d = (f + p) / (f - p)
D (f - p) = d (f + p)
Df - Dp = df + dp
-DP - dp = -Df + df
Dp + dp = Df - df
p(D + d) = Df - df
p = (Df - df) / (D + d)

Well,

I will assume the formula is :
D/d = (f + p)/(f - p)
D/d * (f - p) = f + p
Df/d - pD/d = f + p
Df/d - f = pD/d + p
pD/d + p = Df/d - f
p(D/d + 1) = f * (D/d - 1)
p = f * (D/d - 1)/(D/d + 1)
p = f * (D - d)/(D + d)

qed

hope it' ll help !!

Given: D /d = f + (p / f) - p
Factor out p:

D / d = f + p[(1 / f) - 1]
Subtract out f:

(D / d) - f = p * [(1 / f) - 1]
Divide out the bracketed expression which is multiplied to p:

[(D / d) - f] / [(1 / f) - 1] = p

wah heavy math. I'm sorry, I'm only geade 7 so I cant help