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(Square root of (x+2)+ Square root of (x-2))/( Square root of (x+2)- Square root of (x-2))

(Square root of (x+2)+ Square root of (x-2))/( Square root of (x+2)- Square root of (x-2))
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(Square root of (x+2)+ Square root of (x-2))/( Square root of (x+2)- Square root of (x-2))

(Square root of (x+2)+ Square root of (x-2))/( Square root of (x+2)- Square root of-example-1
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User Citronex
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1 Answer

3 votes

( √(x+2)+ √(x-2) )/( √(x+2)- √(x-2) ) = (( √(x+2)+ √(x-2) )*( √(x+2)+ √(x-2) ) )/( (√(x+2)- √(x-2))*( √(x+2)+ √(x-2) ) ) = ( (√(x+2)+ √(x-2))^2 )/( (√(x+2))^2- (√(x-2))^2 ) = \\ \\ = ( x+2+2 √((x+2)(x-2))+x-2 )/( x+2-(x-2) ) = ( 2x+2 √(x^2-4) )/( x+2-x+2 ) = ( 2(x+√(x^2-4)) )/(4) = ( x+√(x^2-4) )/(2)
answered
User Roxanna
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8.3k points
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