Simplify (y^2-2y+1)/(2y-3)

$\frac{y^{2} - 2 y + 1}{2 y - 3}$

Step 1

Rewrite $1$ as $1^{2}$ .

$\frac{y^{2} - 2 y + 1^{2}}{2 y - 3}$

Step 2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$2 y = 2 \cdot y \cdot 1$

Step 3

Rewrite the polynomial.

$\frac{y^{2} - 2 \cdot y \cdot 1 + 1^{2}}{2 y - 3}$

Step 4

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = y$ and $b = 1$ .

$\frac{{(y - 1)}^{2}}{2 y - 3}$