$$\frac{a}{b}=\frac{c}{d}$$
$$\frac{a}{b}-1=\frac{c}{d}-1$$
$$\frac{a-b}{b}=\frac{c-d}{d}...........(1)$$
$$\frac{a}{b}+1=\frac{c}{d}+1$$
$$\frac{a+b}{b}=\frac{c+d}{d}.........(2)$$
$$(1)\div(2):\frac{a-b}{a+b}=\frac{c-d}{c+d}$$
$$(a-b)(c+d)=(a+b)(c-d)$$
$$ac-bc+ad-bd=ac+bc-ad-bd$$
$$(ad-bc)=-(ad-bc)$$
$$1=-1$$
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