Posted by Gregory on Sunday, May 23, 2010 at 10:37am.
Factor each term; you will find that some terms may cancel out.
For example, x^2 + x = x(x + 1) and x^2 + 3x + 2 = (x + 1)(x + 2).
Also use the properties of fractions with multiplicative inverses:
( (x^2 + x) / (x^2 - 6x + 8) ) / ( (x^2 + 3x + 2) / (2x^2 - 7x + 6) ) =
( (x^2+x) / (x^2 - 6x + 8) ) * ( (2x^2 - 7x + 6) / (x^2 + 3x + 2)
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