Simplify: $$\frac{2}{1 - \sqrt{2}}$$​​

Correct option is A

Solution:

Expression = $$\frac{2}{1 - \sqrt{2}}$$​​

Multiply numerator and denominator by the conjugate of $$(1 - \sqrt{2}):$$​​

Expression = $$\frac{2 \times (1 + \sqrt{2})}{(1 - \sqrt{2}) \times (1 + \sqrt{2})}$$​​

Denominator = $$(1 - \sqrt{2})(1 + \sqrt{2}) = 1 - 2 = -1$$​​

Numerator = $$2 \times (1 + \sqrt{2}) = 2 + 2\sqrt{2}$$​​

Expression = $$-(2 + 2\sqrt{2})$$​​

The simplified expression is $$-2 - 2\sqrt{2}.$$  = -2(1+$$\sqrt2$$)​