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This problem trains for: SAT-I, AMC-8, GMAT, AMC-10.

Find the product of the numbers m and n such that the algebraic fraction:

is reducible by the factor:

Both the numerator and the denominator have to have a factor of x+2.

Both polynomials are quadratic and must have one linear factor. Therefore each must have two linear factors.

Since the leading coefficients are known, the unknown factor at the numerator must be of the form:

but to obtain the desired constant term, we need:

Similarly, the denominator must be:

The product of m and n is: