第2章 2.17

(1)

1xx2=x+x2x(x2)=x+x22\frac{1}{\sqrt{x}-\sqrt{x-2}} = \frac{\sqrt{x}+\sqrt{x-2}}{x-(x-2)} = \frac{\sqrt{x}+\sqrt{x-2}}{2}

(2)

21+2a+12a=2(1+2a12a)(1+2a)(12a)=1+2a12a2a\frac{2}{\sqrt{1+2a}+\sqrt{1-2a}} = \frac{2\left(\sqrt{1+2a}-\sqrt{1-2a}\right)}{(1+2a)-(1-2a)} = \frac{\sqrt{1+2a}-\sqrt{1-2a}}{2a}

a=0a = 0 のとき分母が 00 となり成り立たない

a=0a = 0 のとき 21+1=1\dfrac{2}{\sqrt{1}+\sqrt{1}} = 1

解説: r31bn1z