Vamos simplificar a expressão b:
[tex]b=\sqrt{1-\frac{(x-1)^2}{(x+1)^2}} \\
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b=\sqrt{\frac{(x+1)^2}{(x+1)^2}-\frac{(x-1)^2}{(x+1)^2}} \\
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b=\sqrt{\frac{(x+1)^2-(x-1)^2}{(x+1)^2}} \\
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b=\sqrt{\frac{x^2+2x+1-(x^2-2x+1)}{(x+1)^2}} \\
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b=\sqrt{\frac{x^2+2x+1-x^2+2x-1}{(x+1)^2}} \\
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\boxed{b=\sqrt{\frac{4x}{(x+1)^2}}=\frac{2\sqrt{x}}{x+1}}[/tex]
Agora fazendo:
[tex]\boxed{\frac{a}{b}=\frac{\frac{2}{(x+1)^2}}{\frac{2\sqrt{x}}{x+1}}=\frac{2}{(x+1)^2}.\frac{x+1}{2\sqrt{x}}=\frac{1}{\sqrt{x}(x+1)}=\frac{\sqrt{x}}{x(x+1)}}[/tex]
