Question

Сократите дробь: под номером 2 и 3

Answer 1

$2)\frac{x^{2}-4x+4y-y^{2}}{x^{2}-y^{2}}=\frac{(x^{2}-y^{2})-(4x-4y)}{x^{2}-y^{2}}=\frac{(x-y)(x+y)-4(x-y)}{x^{2}-y^{2}}=\frac{(x-y)(x+y-4)}{(x-y)(x+y)} =\frac{x+y-4}{x+y}=1-\frac{4}{x+y}$

$3)\frac{b^{2}-2b+1-c^{2}}{b^{2}-c^{2}-b+c}=\frac{(b^{2}-2b+1)-c^{2}}{(b^{2}-c^{2})-(b-c)}=\frac{(b-1)^{2}-c^{2}}{(b-c)(b+c)-(b-c)}=\frac{(b-c-1)(b+c-1)}{(b-c)(b+c-1)}=\frac{b-c-1}{b-c}=1-\frac{1}{b-c}$