The algebraic expression that is equivalent to [(x - 1)²/(x² - x - 12)] * [(x² + x - 6)/(x² - 6x + 5)] is; (x² - 3x + 2)/(x² - 9x + 20)
How to solve algebraic fractions?
We are given the algebraic expression;
[(x - 1)²/(x² - x - 12)] * [(x² + x - 6)/(x² - 6x + 5)]
Now, let us simplify each of the quadratic equations;
(x - 1)² = (x - 1)(x - 1)
x² - x - 12 = (x + 3)(x - 4)
x² + x - 6 = (x + 3)(x - 2)
x² - 6x + 5 = (x - 1)(x - 5)
Thus, our original expression can now be rewritten as;
[(x - 1)(x - 1)/((x + 3)(x - 4))] * [(x + 3)(x - 2)/(x - 1)(x - 5)]
Looking at the expression above, we see that (x + 3 ) and (x - 1) will cancel out to give;
[(x - 1)/(x - 4)] * [(x - 2)/(x - 5)]
Multiplying out gives;
(x² - 3x + 2)/(x² - 9x + 20)
Read more about Algebraic Fractions at; https://brainly.com/question/11875858
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