p/q=f/q-f for f

[math_celebrity]

p/q=f/q-f for f

To solve this literal equation for f, let's factor out f on the right side:
p/q=f(1/q-1)

Divide each side by (1/q - 1)
p/(q(1/q - 1)) = f(1/q-1)/(1/q - 1)

Cancelling the (1/q - 1) on the right side, we get:
f = p/(1/q - 1)

Rewriting this since (1/q -1) = (1 - q)/q since q/q = 1 we have:
f = pq/(1 - q)