Question

What is the greatest common factor (GCF) of the numerator and denominatorof the rational expression below?5x - 20/x2 - 2x -8

Answer 1

x-4x-4

Step-by-step explanation:

Given the rational expression;

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

Factorise both the numerator and denominator

`\begin{gathered} (5(x-4))/(x^2-4x+2x-8) \\ =\text{ }(5(x-4))/(x(x-4)+2(x-4)) \\ =\text{ }(5(x-4))/((x+2)(x-4)) \end{gathered}`

Since x-4 is common to both numerator and denominator, hence the GCF is x-4