1 answer

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

Question:

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

Answers

#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)#

.

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