Question

What is the greatest common factor (GCF) of the numerator and denominator of the rational expression below? 5x+10/x^2-x-6 A. x B. x - 3 C. x + 2 D. 5

Answer 1

(5x+10)/(x²-x-6)

1) 5x+10 = 5(x+2)

2) x² - x - 6 = (x+2)(x-3) 6 = -3*2, -1=-3+2

(5x+10)/(x²-x-6) = 5(x+2)/5(x+2)

As we can see greatest common factor is C. x + 2.

Answer 2

The GCF of given rational expression is x+2

C is correct.

Explanation:

Given:
`(5x+10)/(x^2-x-6)`

Here we have rational expression. We need to find the GCF (greatest common factor) of rational expression.

Factor numerator:

`5x+10\Rightarrow 5\cdot x+5\cdot 2`

`5x+10\Rightarrow 5(x+2)`

Factor Denominator:

`x^2-x-6\Rightarrow x^2-3x+2x-6`

`x^2-x-6\Rightarrow (x-3)(x+2)`

Now we will see common factor from numerator and denominator.

`(5x+10)/(x^2-x-6)\Rightarrow (5)/(x-3)`

Common factor is x+2

Hence, The GCF of given rational expression is x+2