Respuesta :
Answer:
GCF = x+3
Step-by-step explanation:
(6x+18)/(x^2-x-12) = 6 (x+3)/(x^2 +3x - 4x -12)
= 6(x+3)/( x(x+3) - 4(x+3) )
= 6(x+3)/( (x-4)(x+3) )
The greatest common factor (GCF) of the numerator and denominator of the rational expression [tex]\frac{(6x+18)}{(x^2-x-12)}[/tex] is (x + 3) .
What is greatest common factor (GCF)?
The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share. For example, 12, 20, and 24 have two common factors: 2 and 4. The largest is 4, so we say that the GCF of 12, 20, and 24 is 4.
According to the question
The rational expression :
[tex]\frac{(6x+18)}{(x^2-x-12)}[/tex]
The greatest common factor (GCF) of the numerator and denominator
Step 1 : We take out factors of numerator
(6x+18) = 6 (x + 3)
Step 2 : Then we take out factors of denominator
[tex](x^2-x-12)[/tex] = x² - (4-3)x - 12
= x² - 4x + 3x - 12
= x (x - 4) + 3(x - 4)
= (x + 3) (x - 4)
Now , The greatest common factor (GCF) of the numerator and denominator is (x + 3) which is present in both .
Hence, the greatest common factor (GCF) of the numerator and denominator of the rational expression [tex]\frac{(6x+18)}{(x^2-x-12)}[/tex] is (x + 3) .
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