The expression (2+{2})+{1}{2+{2}}+{1}{2-{2}} equals:

Correct Answer is : 4+24+{2}4+2

Correct Answer is : 4+24+{2}4+2

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Algebra and Applications Test 3

Question : 12 of 25

Marks: +1, -0

The expression

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

equals:

Solution:

Concept:

Simplify the reciprocal terms by combining them over a common denominator.

Explanation:

Combine the last two terms:

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

The denominator is

(2)^2-(\sqrt{2})^2 = 4-2=2

The numerator is

2-\sqrt{2}+2+\sqrt{2}=4

So the combined fraction is

\frac{4}{2}=2

Now add the first term:

(2+\sqrt{2})+2 = 4+\sqrt{2}

Answer:

4+\sqrt{2}

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