Question

How do you simplify `(2x^2-6x)/(x^2+18x+81) * (9x+81)/(x^2-9)`?

Answer 1

`f(x)=(18x)/(x^2+12x+27)`

Explanation:

We have,
`f(x)=(2x^2-6x)/(x^2+18x+81)*(9x+81)/(x^2-9)`
Now,
`2x^2-6x=2x(x-3)`

`x^2+18x+81=(x)^2+2(x)(9)+(9)^2=(x+9)^2`

`9x+81=9(x+9)`

`x^2-9=(x)^2-(3)^2=(x+3)(x-3)`
So,

`f(x)=(2x(cancel(x-3)))/(cancel((x+9))(x+9)) (9(cancel(x+9)))/((x+3)cancel((x-3)))=(18x)/((x+9)(x+3))`

or `f(x)=(18x)/(x^2+12x+27)`