SOLUTION: I need some help on this one, if f(x)=x^2-81 and g(x)=(x-9)^(-1)(x+9) , find g(x) x f(x)

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Question 1035082: I need some help on this one,

if f(x)=x^2-81 and g(x)=(x-9)^(-1)(x+9) , find g(x) x f(x)
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
x^2 - 81 = (x+9) * (x-9)

(x-9)^(-1) * (x+9) = 1/(x-9) * (x+9) = (x+9) / (x-9)

x+9) * (x-9) * (x+9) / (x-9) = (x+9) * (x+9) = (x+9)^2.

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

how to you know it's good?
use your calculator to evaluate both the original expression and the final expression using a randomly selected value of x.

i used x = 22 (just a number taken off the top of my head).

the display of my calculations of the original expression and the final expression are shown below.

i also calculated x^2 + 18x + 81 using 22 for x and got 22^2 + 18*22 + 81 = 961.

the solution looks good if i understood your problem correctly.