Answer:
The expanded form of [tex](x-\frac{2}{x} ) = \frac{(x+\sqrt2)(x-\sqrt2)}{x}[/tex]
Step-by-step explanation:
Here, the given expression is [tex](x-\frac{2}{x} )[/tex]
Expanding the given :
[tex](x-\frac{2}{x} ) = \frac{x^2-2}{x}[/tex]
Now, by ALGEBRAIC IDENTITY:
[tex](a+b)(a-b) = a^2 - b^2\\\implies(x^2-2) = (x-\sqrt2)(x+\sqrt2)[/tex]
So, the given expression becomes,
[tex]\frac{x^2 -2}{x} = \frac{(x+\sqrt2)(x-\sqrt2)}{x}[/tex]
Hence, the expanded form of [tex](x-\frac{2}{x} ) = \frac{(x+\sqrt2)(x-\sqrt2)}{x}[/tex]
