For some natural numbers $a, b, c$ and $d$ the following equations holds: $$\frac{a}{c}= \frac{b}{d}= \frac{ab + 1}{cd + 1} .$$Prove that $a = c$ and $b = d$.
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Tags: algebra
For some natural numbers $a, b, c$ and $d$ the following equations holds: $$\frac{a}{c}= \frac{b}{d}= \frac{ab + 1}{cd + 1} .$$Prove that $a = c$ and $b = d$.