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