Question

what is the greatest common factor (GCF) of the numerator and denominator of the rational expression below? 3x-15/x^2-x-20

Answer 1

Answer: $(x-5)$

Step-by-step explanation:

The given expression : $\frac{3x-15}{x^2-x-20}$ [Taking as common outside]

$\text{Polynomial in numerator=}3x-15=3(x-5)$

$\text{Polynomial in denominator=} x^2-x-20\\\\=x^2-5x+4x-20\\=-x(x-5)+4(x-5)\\=(x-5)(x+4)$

We can see that the greatest common factor (GCF) of the numerator and denominator of given the rational expression = $(x-5)$