Respuesta :

sqdancefan
[tex]\dfrac{5x-20}{x^{2}-2x-8}=\dfrac{5(x-4)}{(x+2)(x-4)}[/tex]

The greatest common factor of numerator and denominator is (x-4).
kudzordzifrancis
ANSWER

[tex](x - 4)[/tex]

EXPLANATION

The given rational expression is

[tex] \frac{5x - 20}{ {x}^{2} - 2x - 8} [/tex]

The numerator of the given rational expression is

[tex]5x - 20 = 5(x - 4)[/tex]

and the denominator is

[tex] {x}^{2} - 2x - 8[/tex]



We factor the denominator to obtain;


[tex] = {x}^{2} - 4x + 2x - 8[/tex]



[tex] = x(x - 4) + 2(x - 4)[/tex]


[tex] = (x + 2)(x - 4)[/tex]



The greatest common factor of the numerator and the denominator is

[tex](x - 4)[/tex]


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