Section 1.6 : Rational Expressions

For problems 1 – 3 reduce each of the following to lowest terms.

1. $\displaystyle \frac{{{x^2} - 6x - 7}}{{{x^2} - 10x + 21}}$ Solution
2. $\displaystyle \frac{{{x^2} + 6x + 9}}{{{x^2} - 9}}$ Solution
3. $\displaystyle \frac{{2{x^2} - x - 28}}{{20 - x - {x^2}}}$ Solution

For problems 4 – 7 perform the indicated operation and reduce the answer to lowest terms.

1. $\displaystyle \frac{{{x^2} + 5x - 24}}{{{x^2} + 6x + 8}}\,\centerdot \,\frac{{{x^2} + 4x + 4}}{{{x^2} - 3x}}$ Solution
2. $\displaystyle \frac{{{x^2} - 49}}{{2{x^2} - 3x - 5}} \div \frac{{{x^2} - x - 42}}{{{x^2} + 7x + 6}}$ Solution
3. $\displaystyle \frac{{{x^2} - 2x - 8}}{{2{x^2} - 8x - 24}} \div \frac{{{x^2} - 9x + 20}}{{{x^2} - 11x + 30}}$ Solution
4. $\displaystyle \frac{{\displaystyle \frac{3}{{x + 1}}}}{{\displaystyle \frac{{x + 4}}{{{x^2} + 11x + 10}}}}$ Solution

For problems 8 – 12 perform the indicated operations.

1. $\displaystyle \frac{3}{{x - 4}} + \frac{x}{{2x + 7}}$ Solution
2. $\displaystyle \frac{2}{{3{x^2}}} - \frac{1}{{9{x^4}}} + \frac{2}{{x + 4}}$ Solution
3. $\displaystyle \frac{x}{{{x^2} + 12x + 36}} - \frac{{x - 8}}{{x + 6}}$ Solution
4. $\displaystyle \frac{1}{{{x^2} - 13x + 42}} + \frac{{x + 1}}{{x - 6}} - \frac{{{x^2}}}{{x - 7}}$ Solution
5. $\displaystyle \frac{{x + 10}}{{{{\left( {3x + 8} \right)}^3}}} + \frac{x}{{{{\left( {3x + 8} \right)}^2}}}$ Solution