Question

Attachment has question

Answer 1

1/(5x)

Explanation:

You want to simplify the expression ...

((3x +9)/(3x² +12x +9))/((5x² -5x)/(x² -1))

Dividing fractions

As with numerical fractions we can multiply by the inverse of the denominator.

`=(3x+9)/(3x^2+12x+9)*(x^2-1)/(5x^2-x)`

Factors

Factoring the expressions lets us find factors that will cancel. Doing this gives ...

`=(3(x+3))/(3(x+3)(x+1))*((x+1)(x-1))/(5x(x-1))=\boxed{(1)/(5x)}`

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