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`A=(sqrt(x+2sqrt(x-1))+sqrt(x-2sqrt(x-1)))/(sqrt(x+sqrt(2x-1))+sqrt(x-sqrt(2x-1)))*sqrt(2x-1)` `(x>=1)`
`=>A/sqrt2=(sqrt(x-1+2sqrt(x-1)+1)+sqrt(x-1-2sqrt(x-1)+1))/(sqrt(2x-1+2sqrt(2x-1)+1)+sqrt(2x-1-2sqrt(2x-1)+1))*sqrt(2x-1)`
`=>A/sqrt2=(sqrt((sqrt(x-1)+1)^2)+sqrt((sqrt(x-1)-1)^2))/(sqrt((sqrt(2x-1)-1)^2)+sqrt((sqrt(2x-1)+1)^2))*sqrt(2x-1)`
`=>A/sqrt2=(sqrt(x-1)+1+|sqrt(x-1)-1|)/(sqrt(2x-1)-1+sqrt(2x-1)+1)*sqrt(2x-1)`
`=>A/sqrt2=(sqrt(x-1)+1+|sqrt(x-1)-1|)/(2sqrt(2x-1))*sqrt(2x-1)`
`=>A/sqrt2=(sqrt(x-1)+1+|sqrt(x-1)-1|)/2`
`=>A=(sqrt(x-1)+1+|sqrt(x-1)-1|)/sqrt2`
TH1: `sqrt(x-1)>=1`
`<=>x-1>=1`
`<=>x>=2`
`->A=(sqrt(x-1)+1+sqrt(x-1)-1)/sqrt2`
`A=(2sqrt(x-1))/sqrt2`
`A=sqrt(2x-2)`
TH2: `x<2`
`->A=(sqrt(x-1)+1+1-sqrt(x-1))/sqrt2`
`A=2/sqrt2`
`A=sqrt2`
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