Question

约分：[(x^2+y^2-9)^2-4x^2y^2]／(x^2-y^2+6x+9)

Answer 1

利用平方差公式：a^2-b^2=(a+b)(a-b)

分子

=(x^2+y^2-9+2xy)(x^2+y^2-9-2xy)

=((x+y)^2-9)((x-y)^2-9)

=(x+y+3)(x+y-3)(x-y+3)(x-y-3)

分母

=(x+3)^2-y^2

=(x+y+3)(x-y+3)

原式=分子/分母=(x+y-3)(x-y-3)