Question

What is the greatest common factor (GCF) of the numerator and denominator
of the rational expression below?
2x+12/x^2+7x+6

Answer 1

Answer:

C. x + 6

Step-by-step explanation:

Start by factoring completely the numerator and the denominator.

2x + 12 = 2(x + 6)

x^2 + 7x + 6 = (x + 1)(x + 6)

The only common factor is x + 6, so the GCF is x + 6

Answer 2

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.

Learn more about GCF on:

https://brainly.com/question/219464

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