find the limit x-->inf (x^2+x)^1/2-(x^2-x)^1/2 so I know I multiply by the conjugate 2x/(x^2+x)^1/2+(x^2-x)^1/2 then I don't know where to finish problem

Answer 1

√(x^2+x) - √(x^2-x)

(√(x^2+x) - √(x^2-x))(√(x^2+x) + √(x^2-x))
------------------------------------
√(x^2+x) + √(x^2-x)

(x^2+x)-(x^2-x)
-------------------------------
√(x^2+x) + √(x^2-x)

= 2x/(√(x^2+x) + √(x^2-x))

divide top and bottom by x (√x^2)

= 2/(√(1 + 1/x) + √(1 - 1/x))
-> 2/(√1 + √1)
= 2/2
= 1