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If $y=\frac{a x+b}{c x+d}$, than $\frac{d x}{d y}=$
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Verified Answer
The correct answer is:
$\frac{a d-b c}{(a-c y)^2}$
Given $y=\frac{a x+b}{c x+d}$
$\Rightarrow \mathrm{x}=\frac{\mathrm{b}-\mathrm{yd}}{\mathrm{yc}-\mathrm{a}}$
$\text { now } \frac{\mathrm{dx}}{\mathrm{dy}}=\frac{\mathrm{ad}-\mathrm{bc}}{(\mathrm{yc}-\mathrm{a})^2}$
$\Rightarrow \mathrm{x}=\frac{\mathrm{b}-\mathrm{yd}}{\mathrm{yc}-\mathrm{a}}$
$\text { now } \frac{\mathrm{dx}}{\mathrm{dy}}=\frac{\mathrm{ad}-\mathrm{bc}}{(\mathrm{yc}-\mathrm{a})^2}$
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