Answer:
[tex]\frac{x-2}{x}[/tex]
Step-by-step explanation:
given
[tex]\frac{x^2-4}{x+2x}[/tex]
The numerator is a difference of squares and factorises as
x² - 4 = (x - 2)(x + 2)
factor out x from each term on the denominator
x + 2x = x(x + 2)
Then
[tex]\frac{x^2-4}{x+2x}[/tex]
= [tex]\frac{(x-2)(x+2)}{x(x+2)}[/tex] ← cancel the common factor (x + 2)
= [tex]\frac{x-2}{x}[/tex] : x ≠ 0
