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

1 Answer
Mar 18, 2018

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)