: Enter your answer and show all the steps that you use to solve this problem in the space provided.

Simplify the complex fraction.

uu−3+1uu−33

1 answer

To simplify the complex fraction (uu−3+1)/(uu−3+3), we need to first find a common denominator for the numerator and the denominator of the fraction.

Multiply the numerator and denominator by (uu - 3):

[(uu - 3 + 1)(uu - 3)] / [(uu - 3 + 3)(uu - 3)]
= (u^2u - 4u + 3) / (u^2u - 3u -3u + 9)
= (u^2u - 4u + 3) / (u^2u - 6u + 9)

Now simplify the fraction by factoring:

u^2u - 4u + 3 = (u - 3)(u - 1)
u^2u - 6u + 9 = (u - 3)(u - 3)

So the simplified expression is:

(u - 3)(u - 1) / (u - 3)^2
= (u - 1) / (u - 3)