# Honors Algebra 2: Extra Practice on Expressions with Negative Exponents and Sums

• Class: Honors Algebra 2
• Author: Peter Atlas
• Algebra and Trigonometry: Structure and Method, Brown

Calculator Inctive.

Simplify. Include any necessary domain restrictions

1. $$\displaystyle \frac{a^{-1} + b^{-1}}{a^{-1} - b^{-1}}$$
2. Solution

$$\displaystyle \frac{-a - b}{a - b}$$ for $$a,b \ne 0, a \ne b$$

3. $$\displaystyle \frac{2a^{-1} + 3b^{-1}}{3a^{-1} - 2b^{-1}}$$
4. Solution

$$\displaystyle \frac{-3a - 2b}{2a - 3b}$$ for $$\displaystyle a, b \ne 0, a \ne \frac{3b}{2}$$

5. $$\displaystyle \frac{a^{-1} - b^{-1}}{a^{-2} - b^{-2}}$$
6. Solution

$$\displaystyle \frac{ab}{a + b}$$ for $$a, b \ne 0, a \ne b$$

7. $$\displaystyle \left( a + b \right) ^{-1} \cdot \left( a^{-1} + b^{-1} \right)$$
8. Solution

$$\displaystyle \frac{1}{ab}$$ for $$a \ne - b$$

9. $$\displaystyle \left( 2a^{-1} + 3b^{-1} \right)^{-1}$$
10. Solution

$$\displaystyle \frac{ab}{3a + 2b}$$ for $$a, b \ne 0$$

11. Evaluate: $$\displaystyle \frac{-2^{-1}}{2^{-2} + 2^{-3}}$$
12. Solution

$$\displaystyle -\frac{4}{3}$$

13. $$\displaystyle \frac{1 - y^{-1}}{y - y^{-1}}$$
14. Solution

$$\displaystyle \frac{1}{y + 1}$$ for $$y \ne 1, 0$$

15. $$\displaystyle \frac{x^{-1}}{x - x^{-1}}$$
16. Solution

$$\displaystyle \frac{1}{x^2 - 1}$$ for $$x \ne 0$$

17. $$\displaystyle \frac{4 - x^{-4}}{2 - x^{-2}}$$
18. Solution

$$\displaystyle \frac{2x^2 + 1}{x^2}$$ for $$\displaystyle x \ne \pm \frac{1}{\sqrt{2}}$$