Question

arrange the expressions in the correct sequence to rationalize the denominator of the expression -(2)/(\sqrt(x+y-2)-\sqrt(x+y+2))

Answer 1

`(√(x+y-2)+√(x+y+2))/(2)`

Explanation:

Given expression :

`(-2)/(√(x+y-2)-√(x+y+2))`

Now, we solve this expression by rationalizing method

`(-2)/(√(x+y-2)-√(x+y+2))*(√(x+y-2)+√(x+y+2))/(√(x+y-2)+√(x+y+2))`

`(-2(√(x+y-2)+√(x+y+2)))/(x+y-2-x-y-2)`

(using
`(a+b)(a-b)=a^2-b^2`)

`(-2(√(x+y-2)+√(x+y+2)))/(-4)`

`(√(x+y-2)+√(x+y+2))/(2)`

this is the required arrangement which result the expression by rationalizing

Answer 2

We have to rationalize the denominator:

`(-2)/( √(x+y-2) - √(x+y+2) ) = \\ (-2)/( √(x+y-2) - √(x+y+2) )* ( √(x+y-2)+ √(x+y+2) )/( √(x+y-2)+ √(x+y+2) )= \\ (-2*( √(x+y-2)+ √(x+y+2)) )/(x+y-2-(x+y+2))= \\ (-2*( √(x+y-2)+ √(x+y+2)) )/(x+y-2-x-y-2)= \\ (-2*( √(x+y-2)+ √(x+y+2) )/(-4)= \\ ( √(x+y-2)+ √(x+y+2) )/(2)`