[tex]a+b=12\\\dfrac{a-1}{b-1}=\dfrac{2}{3}\\\\a=12-b\\3a-3=2b-2\\3(12-b)-3=2b-2\\36-3b-3=2b-2\\5b=35\\b=7\\\\a+7=12\\a=5[/tex]
[tex]\dfrac{a}{b}=\dfrac{5}{7}[/tex]
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[tex]a+b=12\\\dfrac{a-1}{b-1}=\dfrac{2}{3}\\\\a=12-b\\3a-3=2b-2\\3(12-b)-3=2b-2\\36-3b-3=2b-2\\5b=35\\b=7\\\\a+7=12\\a=5[/tex]
[tex]\dfrac{a}{b}=\dfrac{5}{7}[/tex]