Question

Сократите дробь :
1) a^2-ax/a^2-x^2
2) x^2+2xy+y^2/2x^2-2y^2

Answer 1

1) (a² -ax) /(a² -x²) =a(a -x) /(a -x)(a +x) =a/(a +x)

2) (x² +2xy +y²) /2(x² -y²) =(x +y)² /2(x -y)(x +y) =
=(x +y) /2(x -y)

Answer 2

$frac{a^2-ax}{a^2-x^2}=frac{a(a-x)}{(a-x)(a+x)}=frac{a}{a+x}\\frac{x^2+2xy+y^2}{2x^2-2y^2}=frac{(x+y)^2}{2(x^2-y^2)}=frac{(x+y)^2}{2(x-y)(x+y)}=frac{x+y}{2(x-y)}=frac{x+y}{2x-2y}$