2p - 1/q = r/q + 4, subject q

Solve for q:

2 p - 1/q = r/q + 4

Bring 2 p - 1/q together using the common denominator q. Bring r/q + 4 together using the common denominator q:

(2 p q - 1) / q = (4 q + r) / q

Multiply both sides by q:

2 p q - 1 = 4 q + r

Subtract 4 q - 1 from both sides:

q (2 p - 4) = r + 1

Divide both sides by 2 p - 4:

Answer: q = (r + 1) / (2 p - 4)