Question

simplify:
\frac{u^{2}-2u + 1}{5u^{2}-30u + 25}

Explanation:

Step1: Factor numerator

The numerator $u^2-2u+1$ is a perfect square trinomial, which factors to $(u-1)^2$.
Expression: $u^2-2u+1=(u-1)^2$

Step2: Factor denominator

Factor out the common factor 5 first, then factor the quadratic inside the parentheses: $5u^2-30u+25=5(u^2-6u+5)=5(u-1)(u-5)$.
Expression: $5u^2-30u+25=5(u-1)(u-5)$

Step3: Cancel common factors

Cancel the common $(u-1)$ term from numerator and denominator (where $u
eq1$).
Expression: $\frac{(u-1)^2}{5(u-1)(u-5)}=\frac{u-1}{5(u-5)}$

Answer:

$\frac{u-1}{5(u-5)}$ (or $\frac{u-1}{5u-25}$ when expanded)