Simplify each expression below. If you are stuck, the ideas in problem 7-74 should be helpful.

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

   Hint (a):

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

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   Answer (a):

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

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

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

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

   Hint (b):

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

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