Спростити : [tex] \frac{ \sqrt{x-2 \sqrt{2} } }{ \sqrt{ x^{2}-4x \sqrt{2}+8 } } - \frac{ \sqrt{x+2 \sqrt{2} } }{ \sqrt{ x^{2}+4x \sqrt{2} +8 } } =[/tex]
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√(x²-4x√2+8) √(x²+4x√2+8) √(x-2√2)² √(x+2√2)²
√x-2√2 √x+2√2 √x-2√2
------------ - -------------- = -------------- -1
lx-2√2l x+2√2 lx-2√2l
При х<2√2 , lx-2√2l=-(x-2√2) и имеем:
√х-2√2
---------- =-1 и -1-1= -2
-(√х-2√)
lx-2√2l=x-2√2
x-2√2
--------- = 1 и 1-1=0
x-2√2
Ответ: -2 при х<0; 0,при х≥0.