Question

rewrite \\(\frac{\left((x - 1)^2\
ight)}{x - 1}\\) in lowest terms.

Explanation:

Step1: Rewrite numerator and denominator

Numerator: $(x-1)^2 = (x-1)(x-1)$
Denominator: $x-1$
Expression: $\frac{(x-1)(x-1)}{x-1}$ (for first fraction)

Step2: Cancel common factors

Cancel $(x-1)$ from numerator/denominator, $x
eq 1$
Expression: $x-1$

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Step1: Rewrite exponential terms

Numerator: $(x-1)^2(x+3) = (x-1)(x-1)(x+3)$
Denominator: $(x-1)(x+3)^2(x-2) = (x-1)(x+3)(x+3)(x-2)$
Expression: $\frac{(x-1)(x-1)(x+3)}{(x-1)(x+3)(x+3)(x-2)}$

Step2: Cancel common factors

Cancel $(x-1)$ and $(x+3)$, $x
eq 1, -3, 2$
Expression: $\frac{x-1}{(x+3)(x-2)}$

Answer:

First simplified expression: $x-1$ (where $x
eq 1$)
Second simplified expression: $\frac{x-1}{(x+3)(x-2)}$ (where $x
eq 1, -3, 2$)