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I need help on algebra

 

Find the number of ordered pairs $(a,b)$ of integers such that
\frac{a + 2}{a + 1} = \frac{b}{3}.

 Jun 26, 2024
 #1
avatar+129725 
+1

(a  + 2) / ( a + 1)  = b /3     cross-multiply

 

3(a + 2) = b (a + 1)

 

3a + 6  =  ab + b

 

3a - ab - 1b  + 6  = 0       multiply   the coefficients on a,b = (3)(-1) = -3  and add to both sides

 

3a - ab -1b + 6  - 3 = -3       

 

3a - ab - 1b + 3   =  -3

 

(-a -1)(b -3)  =  -3

 

- (a + 1) ( b -3)  = -3

 

(a + 1) ( b -3) =  3

 

a     b

0     6

2     4

-2    0

-4    2

 

cool cool cool

 Jun 26, 2024

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