Question

помогите решить пожалуйста ​

Answer 1

$1)\frac{x^{2}-2x}{x-3}-\frac{4x-9}{x-3}=\frac{x^{2}-2x-4x+9 }{x-3}=\frac{x^{2}-6x+9 }{x-3}=\frac{(x-3)^{2}}{x-3}=x-3\\\\Otvet:\boxed{x-3}\\\\2)\frac{y^{2} -10}{y-8}-\frac{54}{y-8}=\frac{y^{2}-10-54 }{y-8}=\frac{y^{2}-64}{y-8}=\frac{(y-8)(y+8)}{y-8}=y+8\\\\Otvet:\boxed{y+8}$

$3)\frac{a^{2} }{a^{2}-b^{2}}+\frac{b^{2}}{b^{2}-a^{2}}=\frac{a^{2}}{a^{2}-b^{2}}-\frac{b^{2} }{a^{2}-b^{2}}=\frac{a^{2}-b^{2}}{a^{2}-b^{2}} =1\\\\Otvet:\boxed{1}\\\\4)\frac{x^{2}-2x}{x^{2}-y^{2}}-\frac{2y-y^{2}}{y^{2}-x^{2}}=\frac{x^{2}-2x}{x^{2}-y^{2}}+\frac{2y-y^{2}}{x^{2}-y^{2}}=\frac{x^{2}-2x+2y-y^{2}}{x^{2}-y^{2}}=\frac{(x^{2}-y^{2})-2(x-y)}{x^{2}-y^{2}}=\frac{(x-y)(x+y)-2(x-y)}{x^{2}-y^{2}}=\frac{(x-y)(x+y-2)}{(x-y)(x+y)}=\frac{x+y-2}{x+y}\\\\Otvet:\boxed{\frac{x+y-2}{x+y}}$