Rational Expressions

  1. Simplify the rational expression.  solution

    2. (a) \(\dfrac{x^{2}+3 x+2}{x^{2}-x-2}\)   (b) \(\dfrac{2 x^{2}-x-1}{x^{2}-9} \cdot \dfrac{x+3}{2 x+1}\)  (c) \(\dfrac{\frac{y}{x}-\frac{x}{y}}{\frac{1}{y}-\frac{1}{x}}\)

  2. Simplify.  solution

    3. (a) \(\dfrac{x^3-9x}{2x-6} \)   (b) \(\dfrac{\frac{1}{2+h}-\frac{1}{2}}{h} \)   (c) \(\displaystyle{ \frac{(5+h)^2-25}{h}} \)

  3. Simplify.  solution

    4. (a) \(\dfrac{1}{x}+\dfrac{1}{x-2} \)   (b) \( \dfrac{1}{x+2}-\dfrac{x}{(x+2)(x-2)} \)   (c) \( \dfrac{1}{x^2+x}-\dfrac{1}{x^2-1} \)

  4. Perform the multiplication or division and simplify.  solution

    5. (a) \(\displaystyle \frac{x^2+3 x-40}{x^2-3 x-40} \cdot \frac{8-x}{8+x} \)   (b) \(\displaystyle \dfrac{\frac{2 x^2-9 x-5}{x^2-16}}{\frac{2 x^2+11 x+5}{x^2+x-20}} \)