Moin ak761.

\(\dfrac{x+\sqrt a}{x+ \sqrt b}-\dfrac{x+\sqrt a}{x-\sqrt b}=0\)

\(\Leftrightarrow \dfrac{x+\sqrt a}{x+ \sqrt b}\cdot \dfrac{x-\sqrt b}{x-\sqrt b}-\dfrac{x+\sqrt a}{x-\sqrt b}\cdot \dfrac{x+\sqrt b}{x+\sqrt b}=0\)

\(\Leftrightarrow \dfrac{(x+\sqrt a)(x- \sqrt b)-(x+\sqrt a)(x+\sqrt b)}{(x+\sqrt b)(x-\sqrt b)}=0\)

\(\Leftrightarrow (x+\sqrt a)(x- \sqrt b)-(x+\sqrt a)(x+\sqrt b)=0\)

\(\Leftrightarrow x^2-x\sqrt b-\sqrt{ab}+x\sqrt a- (x^2+x\sqrt b+x\sqrt a+\sqrt{ab})=0\)

\(\Leftrightarrow -2x\sqrt b-2\sqrt{ab}=0\)

\(\Leftrightarrow x=-\sqrt a\)

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