Answer:
GCF: (x - 2)
4 / (x + 5)
Step-by-step explanation:
The expression given is:
(4x - 8) / (x² + 3x - 10)
To find the greatest common factor, we have to factorise the numerator and denominator individually.
NUMERATOR:
4x - 8 = 4(x - 2)
DENOMINATOR:
x² + 3x - 10 = x² + 5x - 2x - 10
x² + 3x - 10 = x(x + 5) - 2(x + 5)
x² + 3x - 10 = (x - 2) ( x + 5)
So, the expression becomes:
4(x - 2) / [(x - 2) ( x + 5)]
We observe that the common factor in both numerator ad denominator is (x - 2).
This is the greatest common factor (GCF).
Factoring out (x - 2), the expression can be rewritten as:
4 / (x + 5)
