### Home > INT3 > Chapter 12 > Lesson 12.1.1 > Problem12-17

12-17.

Simplify each expression below. If you are stuck, use the ideas in problem 12‑16.

1. $\quad \frac { x } { 1 - \frac { 1 } { x } }$

Use a Giant One to eliminate the denominator of the fraction in the denominator.

Distribute:

$\frac{x}{x} \cdot \frac{x}{1-\frac{1}{x}}$

$\frac{1}{x} \cdot x = 1$

$\frac{x^2}{x-1}$

1. $\quad \frac { \frac { 1 } { a } + \frac { 1 } { b } } { \frac { 1 } { b } - a }$

Eliminate all the denominators of the smaller fractions. What will the Giant One look like?

Distribute: $\frac{ab}{ab} \cdot \frac{ \frac{1}{a} - \frac{1}{b} }{ \frac{1}{b} -a}$