Question

Pleease help

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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

Answer 1

Answer:c

Step-by-step explanation:test

Answer 2

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

`( x^(2) -100)/( x^(2) +2x-120) / (6x+60)/(x-2)`

Since
`(a)/(b) / (c)/(d)= (a)/(b) * (d)/(c)= (a*d)/(b*c)`, then:

`( x^(2) -100)/( x^(2) +2x-120) / (6x+60)/(x-2)= ((x^(2) -100)*(x-2))/((x^(2) +2x-120)*(6x+60)) =`

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:

`((x^(2) -100)*(x-2))/((x^(2) +2x-120)*(6x+60)) = ((x-10)(x+10)(x-2))/((x-10)(x+12)*6(x10))`

We can cancel (x-10)(x+10):

`((x-10)(x+10)(x-2))/((x-10)(x+12)*6(x10)) =((x-2))/((x+12)*6) =((x-2))/(6(x+12))`


`(x-2)/(6(x+12))` is quantity x minus 2 over 6 open parentheses x plus 12 close parentheses.