Question

Сократите дробь y^2-2y+1/1-y^2

Answer 1

(у-1)²/(1-у)(1+у)

поскольку (у-1)²=(1-у)²

сокращаем на 1-у и получаем    (1-у) / (1+у) при у ≠1  у≠-1

Answer 2

To simplify the given fraction $\frac{y^2 - 2y + 1}{1 - y^2}$, we first factor the numerator and denominator:

$y^2 - 2y + 1 = (y - 1)^2$

$1 - y^2 = -(y^2 - 1) = -(y - 1)(y + 1)$

Now, we can rewrite the fraction as:

$\frac{(y - 1)^2}{-(y - 1)(y + 1)}$

Next, we can cancel out the common factor of $(y - 1)$ in the numerator and denominator:

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

Finally, we can factor out a negative sign from the denominator to get the simplified form:

$\frac{y - 1}{- (y + 1)} = -\frac{y - 1}{y + 1}$

So, the simplified form of the given fraction is $-\frac{y - 1}{y + 1}$.