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Find the number of ordered pairs $(a,b)$ of integers such that
\frac{a + 2}{a + 1} = \frac{b}{12}.

 Jun 22, 2024
 #1
avatar+1075 
+1

Cross multiplying, we get

\(12a+24=ab+b\)

Moving ab to the other side and factoring, we have

\(a\left(12-b\right)=b-24\)

 

Dividng both sides 12-b, we get

\(a=\frac{b-24}{12-b}\)

 

So, everything works, and we have \(a=\frac{b-24}{12-b};\quad \:b\ne \:12\)

 

So technically, there are infinite solutions. 

 

Thanks! :)

 Jun 22, 2024

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