1. **State the problem:** Simplify the expressions: - $\left(\frac{E}{F} + \frac{8}{9}\right) \frac{E}{M}$ - $x = \left(\frac{r}{E} + \frac{b}{r}\right) \frac{r}{5}$ 2. **Simplify the first expression:** Use the distributive property: $\left(a + b\right)c = ac + bc$ $$\left(\frac{E}{F} + \frac{8}{9}\right) \frac{E}{M} = \frac{E}{F} \cdot \frac{E}{M} + \frac{8}{9} \cdot \frac{E}{M}$$ 3. Multiply the fractions: $$\frac{E}{F} \cdot \frac{E}{M} = \frac{E \cdot E}{F \cdot M} = \frac{E^2}{FM}$$ $$\frac{8}{9} \cdot \frac{E}{M} = \frac{8E}{9M}$$ 4. So the simplified first expression is: $$\frac{E^2}{FM} + \frac{8E}{9M}$$ 5. **Simplify the second expression:** $$x = \left(\frac{r}{E} + \frac{b}{r}\right) \frac{r}{5} = \frac{r}{E} \cdot \frac{r}{5} + \frac{b}{r} \cdot \frac{r}{5}$$ 6. Multiply the fractions: $$\frac{r}{E} \cdot \frac{r}{5} = \frac{r^2}{5E}$$ $$\frac{b}{r} \cdot \frac{r}{5} = \frac{b \cancel{r}}{\cancel{r} 5} = \frac{b}{5}$$ 7. So the simplified second expression is: $$x = \frac{r^2}{5E} + \frac{b}{5}$$