Rational Expressions
1. Simplify the rational expression. solution
(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) \(\dfrac{\frac{y}{x}-\frac{x}{y}}{\frac{1}{y}-\frac{1}{x}}\)
(a) \(\dfrac{x^3-9x}{2x-6} \) (b) \(\dfrac{\frac{1}{2+h}-\frac{1}{2}}{h} \) (c) \(\displaystyle{ \frac{(5+h)^2-25}{h}} \)
(a) \(\dfrac{1}{x}+\dfrac{1}{x-2} \) (b) \( \dfrac{1}{x+2}-\dfrac{x}{(x+2)(x-2)} \) (c) \( \dfrac{1}{x^2+x}-\dfrac{1}{x^2-1} \)