Đáp án:
Giải thích các bước giải:
ĐKXĐ : `x > 0 , x \ne 2`
`P = (xsqrt2)/(2sqrtx+xsqrt2) + (sqrt{2x}-2)/(x-2)`
`= (sqrt2x)/(2sqrtx+sqrt2x) + (sqrt{2x}-2)/(x-2)`
`= (sqrt2x(x-2)+(2sqrtx+sqrt2x)(sqrt2x-2))/((2sqrtx+sqrt2x)(x-2))`
`= (sqrt2x^2-2sqrt2x+2sqrt2x-4sqrtx+sqrt{4x}x-2sqrt2x)/((sqrtx(2+sqrt2x)(x-2))`
`= (sqrt2x^2-4sqrtx+2sqrt{x}x-2sqrt2x)/((sqrtx(2+sqrt2x)(x-2))`
`= (sqrt{2x}x-4+2x-2sqrt{2x})/((sqrtx(sqrt2+sqrt{2x})(x-2))`
`= ((sqrt{2x}+2)(sqrt{x^2}-2))/((2+2sqrt{2x})(x-2))`
`= (sqrt{x^2}-2)/(x-2)`
`= (|x|-2)/(x-2)`
`= (x-2)/(x-2)` (Vì `x > 0` nên `|x| = x`)
`= 1`
