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((sqrt(a^(2)-b^(2))+a)/(sqrt(a^(2)+b^(2)...

`((sqrt(a^(2)-b^(2))+a)/(sqrt(a^(2)+b^(2))+b))-:((sqrt(a^(2)+b^(2))-b)/(a-sqrt(a^(2)-b^(2))))`

Text Solution

Verified by Experts

We have
`(sqrt(a^(2) -b^(2))+a)/(sqrt(a^(2) + b^(2)) + b) div (sqrt(a^(2) + b^(2)) -b)/(a-sqrt(a^(2)-b^(2))) = (a+sqrt(a^(2)-b^(2)))/(sqrt(a^(2) + b^(2))+b) xx(a-sqrt(a^(2)+b^(2)))/(sqrt(a^(2)+b^(2))-b)`
`=((a)^(2) - sqrt((a^(2) + b^(2)))^(2))/(sqrt((a^(2) + b^(2))^(2) - (b)^(2))) `
`=(a^(2) -(a^(2) -b^(2)))/((a^(2) + b^(2))-b^(2)) = (a^(2) -a^(2)+b^(2))/(a^(2) + b^(2) -b^(2)) = (b^(2))/(a^(2))`
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