Chapter 10 - Systems of Equations and Inequalities - Section 10.6 Systems of Nonlinear Equations - 10.6 Assess Your Understanding - Page 795: 78

$\frac{1}{7}$

1. Based on the given conditions, we have $\begin{cases}\frac{a}{b}=\frac{4}{3} \\ a+b=14 \end{cases}$ 2. The 1st equation gives $a=(\frac{4}{3})b$ use it in the 2nd equation to get $(\frac{4}{3})b+b=14$, thus $b=6$, use the 1st equation to get $a=8$ 3. We have $\frac{a-b}{a+b}=\frac{2}{14}=\frac{1}{7}$