Ta có:\(\dfrac{a}{3}-\dfrac{1}{2}=\dfrac{1}{b+5}\)
\(\Rightarrow\dfrac{2a}{6}-\dfrac{3}{6}=\dfrac{1}{b+5}\)
\(\Rightarrow\dfrac{2a-3}{6}=\dfrac{1}{b+5}\)
\(\)Ta có:\(\dfrac{2a-3}{6}=\dfrac{1}{b+5}\)
\(\Rightarrow\left(2a-3\right).\left(b+5\right)=6\left(6.1=6\right)\)
\(\Rightarrow2a-3\inƯ\left(6\right)\)
\(Ư\left(6\right)=\left\{1;2;3;6;-1;-2;-3;-6\right\}\)
Mà 2a-3 là số lẻ\(\Rightarrow2a-3\in\left\{1;3;-1;-3\right\}\)
\(\Rightarrow2a\in\left\{4;6;2;0\right\}\)
\(\Rightarrow a\in\left\{2;3;1;0\right\}\)
*Khi a=2,ta có:(2.2-3).(b+5)=6
1.(b+5)=6
b+5=6
b=1
*Khi a=3,ta có:(2.3-3).(b+5)=6
3.(b+5)=6
b+5=2
b=-3
*Khi a=1,ta có:(2.1-3).(b+5)=6
(-1).(b+5)=6
b+5=-6
b=-11
*Khi a=0,ta có:(2.0-3).(b+5)=6
(-3).(b+5)=6
b+5=-2
b=-7
Vậy a=2;b=1
a=3;b=-3
a=1;b=-11
a=0;b=-7