How to find equal gcd for polynomials? In one of my previous questions for finding a value n so that the fraction isn't in the simplest form, the answer stated that $\gcd(2x+5,3x+4) = \gcd(2x+5,x−1)$.
Can anyone explain how the answerer (who I'm very thankful to) arrived at this?
Thank you!

The greatest common divisor of the leading coefficients of both expressions, that is, $\gcd (3,2)=1$. 
So, $$3x+4-(1)(2x+5) = x-1$$ This is called the Euclidean Algorithm. Hope it helps. 
