Question 34

Simplify the value of $$1-\frac{1}{1+\sqrt{2}}+\frac{1}{1-\sqrt{2}}$$ is

Solution

Expression : $$1-\frac{1}{1+\sqrt{2}}+\frac{1}{1-\sqrt{2}}$$

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

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

= $$1-2\sqrt{2}$$

=> Ans - (B)

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