One ratio given in letters: express another ratio in those letters

1. A.
   $\frac{a^2}{\sqrt{b^2 - a^2}}$
2. B.
   $\frac{b^2 - a^2}{ab}$
3. C.
   $\frac{a^2}{b\sqrt{b^2 + a^2}}$
4. D.
   $\frac{a^2}{b\sqrt{b^2 - a^2}}$

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1. A.
   $\frac{\alpha}{\sqrt{1 - \alpha^2}}$
2. B.
   $\frac{\alpha}{\sqrt{1 + \alpha^2}}$
3. C.
   $\frac{\sqrt{1 + \alpha^2}}{\alpha}$
4. D.
   $\frac{\sqrt{1 - \alpha^2}}{2\alpha}$

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1. A.
   $\frac{n^2}{m\sqrt{n^2 - m^2}}$
2. B.
   $\frac{m^2}{n\sqrt{m^2 - n^2}}$
3. C.
   $\frac{m^2}{n\sqrt{n^2 - m^2}}$
4. D.
   $\frac{n^2}{m\sqrt{m^2 - n^2}}$

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1. A.
   $\frac{y}{\sqrt{x^2+y^2}}$
2. B.
   $\frac{x}{\sqrt{x^2+y^2}}$
3. C.
   $\frac{x}{\sqrt{x^2-y^2}}$
4. D.
   $\frac{y}{\sqrt{x^2-y^2}}$

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1. A.
   $\frac{n^2}{n^2 - m^2}$
2. B.
   $\frac{2n^2}{n^2 - m^2}$
3. C.
   $\frac{n^2}{2(n^2 - m^2)}$
4. D.
   $\frac{5n^2}{n^2 - m^2}$

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1. A.
   $\frac{1 + x^2}{1 - x^2}$
2. B.
   $\frac{1 - x^2}{1 + x^2}$
3. C.
   $\frac{2x}{1 - x^2}$
4. D.
   $\frac{1 - x^2}{2x}$

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1. A.
   $1 - x^2$
2. B.
   $2 - x^2$
3. C.
   $3 - x^2$
4. D.
   $1 - 2x^2$

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1. A.
   $\frac{\sqrt{n^2 - m^2}}{n}$
2. B.
   $\frac{m}{\sqrt{n^2 - m^2}}$
3. C.
   $\frac{n}{\sqrt{n^2 - m^2}}$
4. D.
   $\frac{\sqrt{m^2 - n^2}}{n}$

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1. A.
   $\frac{x}{\sqrt{(1-x^2)}}$
2. B.
   $\frac{\sqrt{(1-x^2)}}{x}$
3. C.
   $\frac{1}{x}$
4. D.
   $x^2$

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1. A.
   $\sqrt{1 - x^2}$
2. B.
   x
3. C.
   $\frac{1}{x}$
4. D.
   Undefined

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1. A.
   $\frac{2x}{(1-x^2)}$
2. B.
   $x$
3. C.
   $\frac{1}{x}$
4. D.
   $\frac{(1-x^2)}{2x}$

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