Question

Сократите дроби: x^2-2x+1/x^2-1

Answer 1

(х-1)^2/ (х+1)(х-1) = х-1/х+1

Answer 2

To simplify the fraction $\frac{x^2-2x+1}{x^2-1}$, we can factor both the numerator and the denominator:

Numerator: $x^2-2x+1$ can be factored as $(x-1)^2$.

Denominator: $x^2-1$ is a difference of squares and can be factored as $(x+1)(x-1)$.

Now, we can cancel out the common factor $(x-1)$ from the numerator and denominator:

$\frac{x^2-2x+1}{x^2-1} = \frac{(x-1)^2}{(x+1)(x-1)}.$

Since $(x-1)$ is in both the numerator and denominator, it cancels out, leaving us with:

$\frac{(x-1)^2}{(x+1)(x-1)} = \frac{1}{x+1}.$

So, the simplified fraction is $\frac{1}{x+1}$.