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When defined, the expression (x^2-y^2)/(xy)-(xy-y^2)/(xy-x^2

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by fskilnik@GMATH » Sun Mar 03, 2019 1:19 pm

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GMATH practice exercise (Quant Class 3)

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Answer: [spoiler]_____(A)__[/spoiler]
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by fskilnik@GMATH » Sun Mar 03, 2019 3:18 pm
fskilnik@GMATH wrote:GMATH practice exercise (Quant Class 3)

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$$? = \frac{{{x^2} - {y^2}}}{{xy}} - \frac{{xy - {y^2}}}{{xy - {x^2}}}\,\,\,$$
$$\frac{{xy - {y^2}}}{{xy - {x^2}}} = \frac{{y\left( {x - y} \right)}}{{x\left( {y - x} \right)}} = \underleftrightarrow {\frac{{ - y\left( {y - x} \right)}}{{x\left( {y - x} \right)}}} = \frac{{ - y}}{x}$$
$$? = \frac{{{x^2} - {y^2}}}{{xy}} + \frac{y}{x} = \underleftrightarrow {\frac{{{x^2} - {y^2}}}{{xy}} + \frac{{y \cdot y}}{{x \cdot y}} = \frac{{{x^2}}}{{xy}}} = \frac{x}{y}\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\left( A \right)$$

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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