The greatest common factor of the numerator and denominator is (x+6).
What is the greatest common factor?
The biggest positive integer that divides evenly into all the numbers with no remainder is the greatest common factor of a collection of whole numbers.
Given rational expression:
2x + 12 / (x^2 + 7x + 6)
2(x + 6) / (x^2 + 6x + x + 6) (on factorizing)
2(x + 6) / (x(x + 6) + 1(x + 6))
2(x + 6) / (x + 6)(x + 1)
On factorizing it is clearly visible that the GCF is (x + 6) as it is present in both numerator and denominator and will leave a remainder of zero when used as a divisor.
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