Chapter 1 - Equations and Inequalities - 1.6 Other Types of Equations and Applications - 1.6 Exercises - Page 148: 100

$\{-\frac{7}{4},\frac{1}{2} \}$

Step 1. Let $u=(x)^{-1}$, we have $7u^2-10u-8=0$ Step 2. Factor and solve: $(u-2)(7u+4)=0$ thus $u=-\frac{4}{7}, 2$ Step 3. For $u=-\frac{4}{7}$, we have $(x)^{-1}=-\frac{4}{7}$ thus $x=-\frac{7}{4}$ Step 4. For $u=2$, we have $(x)^{-1}=2$ thus $x=\frac{1}{2}$ Step 5. Solution set $\{-\frac{7}{4},\frac{1}{2} \}$