Compound fractions.

 

Simplify \[ \frac{\dfrac{1}{x} - 1}{ 1 + \dfrac{1}{x}} \ \]

Put numerator and denominator over their common denominators.

\[ = \frac{\dfrac{1 - x}{x} }{\dfrac{1 + x}{x}} \ \]

Multiply the numerator by the reciprocal of the denominator.

\[ = \frac{1 - x}{x} \times \frac{x}{1 + x} \ \]

Cancel common factors.

\[ = \frac {1-x} {1+x} \ \]

You will gain most benefit if you work through each problem first and then come back and check your work against the solution.

 

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Now You Try:

Simplify \[ \frac{\dfrac{1}{x+1} - 1}{ 1 + \dfrac{1}{x+1}} \ \]