Multiply & divide rational expressions (advanced)

Problem

The following equation is true for all real values of n for which the expression on the left is defined, and A is a polynomial expression.
start fraction, n, start superscript, 2, end superscript, plus, 24, n, plus, 144, divided by, n, start superscript, 2, end superscript, plus, 11, n, minus, 12, end fraction, dot, start fraction, n, start superscript, 2, end superscript, plus, 2, n, minus, 3, divided by, A, end fraction, equals, 1
What is A?
A, equals
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