The answer is <span>quantity x minus 2 over 6 open parentheses x plus 12 close parentheses.
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quantity x squared minus 100 (x² - 100) over quantity x squared plus 2 x minus 120 (x² + 2x - 120)<span> divided quantity 6 x plus 60 (6x + 60) over quantity x minus 2 (x - 2) can be expressed as
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Since </span>
, then:
Let's simplify some of the factors:
* x² - 100 = x² - 10² = (x - 10)(x + 10) (since a² - b² = (a - b)(a + b))
* 6x + 60 = 6 * x + 6 * 10 = 6 * (x+10)
* x² + 2x - 120 = x² + 12x - 10x - 12 * 10 = (x * x - 10 * x) + (12 * x - 12 * 10) =
= x(x - 10) + 12(x - 10) = (x - 10)(x + 12)
Now substitute this into the expression:
We can cancel (x-10)(x+10):
is quantity x minus 2 over 6 open parentheses x plus 12 close parentheses.