Question

Simplify 2+√5/2-√5 + 2-√5/2+√5

Answer 1

Answer:

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The only clear way to solve it successfully is by making the two fractions’ denominators one. And the easy way to do that in your case to multiply the first by 2+√5 and the second by 2-√5. So, you obtain:

(2+√5/2-√5) + (2-√5/2+√5)= ((2+√5)*(2+√5)/(2-√5)*(2+√5)) + ((2-√5)*(2-√5)/(2+√5)*(2-√5))= ((2+√5)²+(2-√5)²)/((2+√5)*(2-√5))=((4+5+4√5)+(4+5–4√5))/(2²-√5²)=(9+9+4√5–4√5)/(4–5)=18/(-1)= -18

The mathematical properties used:

(a+b)²=a²+2ab+b² , (a-b)²=a²-2ab+b² and (a+b)*(a-b)=a²-b²

Hope it's helpful......... ☺

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Answer 2

Answer:

-18

Step-by-step explanation

2+√5/2-√5+2-√5/2+√5

rationalize both numeration and denominator we get

(2+√5)^2/4-5+(2-√5)^2/4-5

4+5+4√5+4+5-4√5/-1

18/-1

-18