Let m and n be numbers that differ by 2, and write the sum  as a fraction in lowest terms....

Let m and n be numbers that differ by 2, and write the sum  as a fraction in lowest terms. For example,

 (a) Compute the next three examples.

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(b) Examine the numerators and denominators of the fractions in (a) and compare them with the table of Pythagorean triples on page 18. Formulate a conjecture about such fractions.

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(c) Prove that your conjecture is correct.