[tex]\rm \dfrac12=\dfrac{a+b}{a-b}[/tex]
Let's multiply both sides by 2,
[tex]\rm 1=2\dfrac{a+b}{a-b}[/tex]
and then multiply both sides by (a-b),
[tex]\rm a-b=2(a+b)[/tex]
distribute the 2,
[tex]\rm a-b=2a+2b[/tex]
add b to each side,
and subtract 2a from both sides,
[tex]\rm a-2a=b+2b[/tex]
[tex]\rm -a=3b[/tex]
[tex]\rm a=-3b[/tex]
divide by b to find the ratio,
[tex]\rm \dfrac{a}{b}=-3[/tex]
Hope that helps! :)
