Pleease
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simplify completely quantity x squared minus 100 over quantity x squared plus 2 x minus 120 divided quantity 6 x plus 60 over quantity x minus 2.

quantity x minus 1 over 6 open parentheses x plus 6 close parentheses

quantity x minus 2 over 6 open parentheses x plus 10 close parentheses

quantity x minus 2 over 6 open parentheses x plus 12 close parentheses

quantity x minus 1 over 3 open parentheses x plus 12 close parentheses

The answer is quantity x minus 2 over 6 open parentheses x plus 12 close parentheses.


quantity x squared minus 100 (x² - 100) over quantity x squared plus 2 x minus 120 (x² + 2x - 120) divided quantity 6 x plus 60 (6x + 60) over quantity x minus 2 (x - 2) can be expressed as


Since , 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.