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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!

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    $\gcd(a,b)=\gcd(a,b-a)$ – 2017-02-21

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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.

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    @BillDubuque Thanks for editing. – 2017-02-21