How do you do this problem?

Question

How do you simplify (u^2-u+6)(u+2)^-2 I really need help ive been stuck on this problem for many weeks.

Answer 1

(u^2-u+6)(u+2)^(-2):

First factor (u^2-u+6) = (u-3)(u+2)

Now (u+2)^(-2) = 1 / (u+2)^2

so

(u^2-u+6) (u+2)^(-2) = (u-3)(u+2) / (u+2)^2 = (u-3) / (u+2)

Answer 2

The first factor (u^2 - u + 6) can be factored to: (u - 3)(u + 2)

the second factor (u + 2) ^(-2) is the same as: 1/(u + 2)^2

so the expression can be written as

(u - 3)(u + 2)/(u + 2)^2

Common factor of (u + 2) in numerator and denominator = 1

so,

(u - 3)/(u + 2) is final expression simplified