Answer
$\frac{a-1}{b}=\frac{c-1}{d}$
Work Step by Step
Step 1. Evaluate the left composite: $f(g(x))=f(cx+d)=a(cx+d)+b=acx+ad+b$
Step 2. Evaluate the right composite: $g(f(x))=g(ax+b)=c(ax+b)+d=acx+bc+d$
Step 3. With $f(g(x))=g(f(x))$, we have: $acx+ad+b=acx+bc+d$ or $ad-d=bc-b$ which gives $(a-1)d=b(c-1)$ or in the form of ratios $\frac{a-1}{b}=\frac{c-1}{d}$
