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

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 \( a,b \ne 0, a \ne b\)

  2. \( \displaystyle \frac{2a^{-1} + 3b^{-1}}{3a^{-1} - 2b^{-1}}\)
    3. Solution

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

  3. \( \displaystyle \frac{a^{-1} - b^{-1}}{a^{-2} - b^{-2}}\)
    4. Solution

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

  4. \( \displaystyle \left( a + b \right) ^{-1} \cdot \left( a^{-1} + b^{-1} \right) \)
    5. Solution

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

  5. \( \displaystyle \left( 2a^{-1} + 3b^{-1} \right)^{-1} \)
    6. Solution

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

  6. Evaluate: \( \displaystyle \frac{-2^{-1}}{2^{-2} + 2^{-3}}\)
    7. Solution

    \( \displaystyle -\frac{4}{3} \)

  7. \( \displaystyle \frac{1 - y^{-1}}{y - y^{-1}} \)
    8. Solution

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

  8. \( \displaystyle \frac{x^{-1}}{x - x^{-1}} \)
    9. Solution

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

  9. \( \displaystyle \frac{4 - x^{-4}}{2 - x^{-2}}\)
    10. Solution

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