Question

which is the greatest common factor of the numerator and denominator of the rational expression below? 5x-20/x^2-2x-8

Answer 1

ANSWER


`(x - 4)`

Step-by-step explanation

The given rational expression is


`\frac{5x - 20}{ {x}^(2) - 2x - 8}`

The numerator of the given rational expression is


`5x - 20 = 5(x - 4)`

and the denominator is


`{x}^(2) - 2x - 8`



We factor the denominator to obtain;



`= {x}^(2) - 4x + 2x - 8`




`= x(x - 4) + 2(x - 4)`



`= (x + 2)(x - 4)`



The greatest common factor of the numerator and the denominator is


`(x - 4)`

Answer 2

`(5x-20)/(x^(2)-2x-8)=(5(x-4))/((x+2)(x-4))`

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