Solutions To Mathematics Textbooks/Calculus Early Transcendentals (6th) (0495011665)/Chapter 1.1

=Chapter 1.1 Exercises=

25
Replace instances of $$f(x)\,$$ with the expression $$\frac{1}{x}$$.

$$ \frac{\frac{1}{x}-\frac{1}{a}}{x-a} = \left( \frac{1}{x}-\frac{1}{a} \right) \cdot \frac{1}{x-a} $$

$$ = \frac{a-x}{xa(x-a)} = \frac{(a-x)}{-xa(a-x)} = -\frac{1}{ax} $$