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jmc

algebra junior

Problem

Evaluate:

(\frac{1}{2} + \frac{1}{3}) (\frac{1}{2} - \frac{1}{3})

Solution

For any

x

and

y

,

(x + y) (x - y) = x^{2} - y^{2} + x y - x y = x^{2} - y^{2}

, so

(\frac{1}{2} + \frac{1}{3}) (\frac{1}{2} - \frac{1}{3}) = (\frac{1}{2})^{2} - (\frac{1}{3})^{2} = \frac{1}{4} - \frac{1}{9} = \frac{9}{36} - \frac{4}{36} = \frac{5}{36}

Final answer

\frac{5}{36}